This is certainly an interesting question, and it's actually one that's not especially straightforward to answer. To begin with, while it's true that the early modern English fire insurance system has been well-studied, not least by Trebilcock and Pearson, its chroniclers have always been economic historians who were a lot more interested in the economic aspects of the insurance business than in the practicalities of what one would do if, having taken out insurance, either you or your neighbours suffered an actual fire.

This problem has been further exacerbated by the many popular sources available online, most of which seem very taken by the comic opportunities apparently presented by the system that prevailed in London between the Great Fire of 1666 and the creation of the first proper metropolitan fire service in London in 1833. This 150+-year period saw much London firefighting effectively privatised and left in the hands of rival fire insurance companies, each of which maintained its own small fire-fighting service. You don't have to look too far online to find sources (including the one maintained by the current London fire brigade) that suggest that these competing groups of fire-fighters would simply refuse to tackle blazes in properties that didn't happen to be insured by them, and that, on occasion, several different crews of professional firemen would simply stand back and watch while fire ran out of control, intervening only if it reached a property that was actually insured by them. Similarly, it's pretty regularly asserted that, if you happened to own an insured home and a blaze broke out in a property owned by an uninsured neighbour, it was no use summoning your private fire brigade to tackle that blaze and so protect your own property. They would only go into action when your home actually caught fire.

The reality was rather different. The Great Fire left a very deep imprint on the collective memories of Londoners. It had been hideously destructive, obliterating around 13,000 homes, 87 churches (including St Paul's cathedral), 52 guild halls and Newgate Prison as it raged, and it left about a fifth of the city's population homeless. The result, as London historian Jerry White points out, was that an "understandable paranoia" about fire prevailed among the people of succeeding generations, and that fire remained "one of the great anxieties of the age". It was simply inconceivable, in such circumstances, that Londoners of any sort would simply allow a fire to rage unchecked, no matter what the financial situation that prevailed, and in fact the evidence rather strongly suggests that the image of private fire-fighters standing idly by while a blaze got seriously out of hand simply never actually happened.

Let's begin this response at the beginning, though. Your presumption that you would be able to insure your London property adequately against fire so early as 1670 is incorrect. The first modern fire insurance company was not created until 1681, when an enterprising London doctor named Nicholas Barbon launched his Insurance Office for Houses, and it was not until two rival mutual schemes, the Friendly Fire Office and the Amicable Contributorship (nicknamed the Hand-in-Hand), got underway in 1683 and 1696 respectively that the first private fire brigades actually came into existence. All in all, therefore, the creation of a workable insurance system that might actually help you to extinguish a fire in your property thus need to be dated to closer to 1700 than 1670. This dating is rather interesting, because from March 1708 London ordinances mandated that every parish in the city should maintain its own fire engine, "and also a hand engine" which could "throw up water for the extinguishing of fires", and which it was required to keep in "good order and repair". Many parishes, it appears, had maintained a firefighting service of their own before this date, but it was this ordinance that regulated the system and set required standards for it – for example, every parish was henceforth required to possess a leather hose of the right size to plug into London's system of water mains, which could "without loss or help of bucket" replenish the reservoir of water in the engines. From this date, every parish also employed an engine keeper, who was paid a bonus of 30 shillings if his engine was the first to attend a fire, and paid 10s. rewards to "turncocks" who had the job of turning on the water supply in the vicinity of a fire. There was, thus, only a really rather short period of perhaps 10 or 15 years during which a fire might break out in London and be attended by a private fire brigade alone, and even before 1708 this must have been a rare, if not actually unheard-of, occurrence.

Let's assume, though, that you are a Londoner in this period, decided to take out proper insurance, and were unlucky enough to suffer a fire. If the blaze began by day, you, or more probably a servant, would most likely notice it in time to extinguish it yourselves, or with the assistance of neighbours. If it broke out by night – or during the day in high summer and in a period when winds were high and fire spread quickly – then it was the duty of the members of the city watch to raise the alarm, which they'd typically do by ringing the bells of the nearest parish church. It was this ringing that would alert both the parish fire brigade and the private fire services of the period to the existence of the fire. What wouldn't happen, apparently, is any sort of attempt by the householder or his servants to directly notify their insurance office that they were in need of help. These, in fact, kept normal office hours and don't seem to have maintained any sort of out-of-hours emergency service.

Nonetheless, the ringing of church bells would have been an effective alert for the parish fire brigade, together with the parish constable and beadles, whose duties also including attending fires. All these people would certainly be able to distinguish the bells of their parish church from those of neighbouring parishes. They would have needed help to locate the actual blaze – the signal certainly did not communicate the exact address of the conflagration, nor the identity of the properties that were on fire – but proximity would have ensured that, in most cases, the parish engine would probably arrive at the site of a fire first. It certainly appears that, subsequently, several different private fire brigades might also converge on the scene, and that their crews would also attempt to assist if the fire was a serious one. The insurance crews might, indeed, have been more effective fire-fighters than the parish men – private insurance companies typically contracted this work out to moonlighting Thames watermen, who supplemented their normal incomes in this manner.

Thus no fire that took place in London would have been left to burn unchecked. Moreover, while, in theory, the fire services maintained by the private insurance companies would only assist in extinguishing fires in premises insured by them, it seems that in practice very few private engines attended a fire, discovered it had originated in an uninsured property, and then did nothing about it. By the middle of the 18th century, at the latest, rival insurance groups had established formal reciprocal arrangements under which their crews would tackle fires in properties insured by other companies, to be reimbursed by the insurer later, and private brigades might also combine forces to tackle any significant blaze that threatened to get out of hand and cause significant damage over any wide area.

The sort of chaos implicit in the existence of private fire services thus appears to have been very largely avoided in Georgian London, and we can, I think, read quite a bit into the financial success of the insurance system that was established in this period. Pearson puts the value of property insured across the whole of Britain in 1725 at about £31m. This total rose rapidly. By 1782, according to estimates made for the Prime Minister, Lord North, about £150m of British property was insured against fire. It was clearly in the best interests of the wealthy financial sector that was thus created to keep the actual damage caused by fire to a minimum, and it seems inconceivable that such a powerful business would have been content to allow the comically-inept firefighting operations envisaged in many popular histories of London to have put at risk so much of their capital. It's also telling that, after 1666, the next really major "fire of London" did not take place till 1861, when a blaze that started in a warehouse district in Tooley Street, near London Bridge, got badly out of control.

I had to write this on my mobile as I'm away from home without my references, or my laptop. I apologise for the mess.

Prior to 1666 (Great Fire of London for anyone unfamiliar) the fire brigade didn't exist. In reaction to the Great Fire of London savvy entrepreneurs such as Nicholas Barbon began offering a new product to Londoners, insurance. In 1681 Barbon set up the first such company, it was called Fire Office. It is my understanding that this insurance covered them against multiple types of damage to their property, however fire was the most common (please someone correct me if I'm wrong). Insurance fire brigades weren't the only potential brigades I am aware of voluntary and parish based brigades existing too and records ar found for them prior to 1666, but they primarily had buckets, or a six pint "fire engine", or equipment to pull a building down to stop the fire. It was quickly established that this market was incredibly profitable and more and nor insurance companies were set up.

Now to answer your latter question you and I are neighbours. I'm insured by Phoenix and you're insured by Hand in Hand. Well as it's 1670 and neither exist we're both going to get no help from them, instead we'll be putting our fires out ourselves, with the help of servants, neighbours, the parish fire service, and any volunteer fire service. Now let's jump forward to 1700 as well better setting for your question - presuming you want a useful answer rather than a facetious one. There's a huge variance in answers here, the most commonly heard is that everyone would sit around and ignore it unless it was a fire in one of their insured houses. However it's not this simple, no one wants a repeat of 1666 and by 1700 the majority of fires are happening in houses that haven't been rebuilt with stone etcetera so many fires did still spread wiping out whole neighbourhoods. Some sources suggest that Phoenix would put out the fire for me the paying customer and you my neighbour, however they'd expect to be paid by Hand in Hand in the stead of Hand in Hand paying their own fire brigade who didn't turn up. - I can't quite recall the source for this off the top of my head but can upon my return home in the morning few weeks.

It's noteworthy that these men would have worn bright uniforms that were distinct from one another (company not individuals within the same company) as this is potential evidence that other fire brigades would have turned up to each fire. These men weren't well trained, I remember reading that some were Thames Watermen (so ferry operators, because obviously they know about water so what more does one need?).

In terms of your first question how they knew, that one I don't know as much about, I would posit that the systems in place prior to 1666 were still in use and that London being far more level with less light pollution made it far easier to see fires. I know that the local parish would ring bells but I'm not sure on who informed anyone to begin this. Once these bells began to ring you'd have the scenario I mentioned above in our 1670 event, neighbours, parish police (because crime and fire officials were parish based, there's no Met for the next 200 years), the parish fire brigade that existed pre 1666 are all helping to put out the fire and avoid it devastating the parish. I do have an inkling from a source I can't remember that fire brigades would all rush to fires in case it was one of their's, they're only paid then by the insurance company if they put out or attend these fires. So the fire brigades were incentivised to get to any and all fires quickly. Additionally they'd be checking whether any neighbouring properties were insured by them and at risk of catching fire, however again sources suggest they wouldn't help putting out the original fire, and would wait until yours began to light.

I did research who exactly would inform the bell ringers, and what chain of command is, but I suppose in a fire it's a crisis rather than a routine set of plans. In my research I had a skim through some of Pepys' diary entries to see what I could find about fires after 1666.

"When between two and three in the morning we were waked with my maids crying out, “Fire, fire, in Markelane!” So I rose and looked out, and it was dreadful; and strange apprehensions in me, and us all, of being presently burnt. So we all rose; and my care presently was to secure my gold, and plate, and papers, and could quickly have done it, but I went forth to see where it was; and the whole town was presently in the streets; and I found it in a new-built house that stood alone in Minchin-lane, over against the Cloth-workers’-hall, which burned furiously: the house not yet quite finished; and the benefit of brick was well seen, for it burnt all inward, and fell down within itself; so no fear of doing more hurt... saw the fire, which spent itself, till all fear over"

I also found this source that suggests the house owners had to raise the alert with a mention of night watchmen, but I don't particularly rate it as a source:

"The Stuarts – Fire and Fire – Fighting" History on the Net © 2000-2021, Salem Media. January 3, 2021 https://www.historyonthenet.com/the-stuarts-fire-and-fire-fighting

That states: "Householders were instructed to investigate any smell of smoke and raise the alarm if necessary.

At night it was the night-watchman’s job to guard against fire and in hot weather householders were often told to leave buckets of water outside their doors in case of fire. "

However it mentions 1620 being the policy regarding houses being built from stone, and that reads as them conflating a Royal Proclamation from 1620 about dangerous houses with the 1667 rebuilding act. No sources are mentioned in that source either so I would not pay it too much attention.

Aviva (a descendent, through many a merge, of Hand in Hand Life and Fire Insurance) does imply that people might reach out directly to their insurance company's fire brigade, they don't mention a source but I'd assume it's a primary source of their own, their archive states the following:

"In 1699, the company began to employ watermen to act as firefighters. Initially, six watermen were employed and given blue uniforms lined with red. The names and addresses of the members of this fire brigade were listed so that policyholders would know who to turn to in the event of a fire".

In regard to the chances of your house catching, as mentioned in the Pepys diary is appeared some fires burnt themselves out without causing damage elsewhere.

Moreover 1666 led to a great number of changes as much of London was rebuilt The Fire Prevention Regulations, printed by the City of London in 1668 stated "That plugs be put into the pipes in the most convenient places or every street, whereof all inhabitants may take notice, that breaking of the pipes in disorderly manner maybe avoided" (I've copied this verbatim as I have no idea what this means, I studied history rather than town planning) prior to this pipes had been made of wood. Additionally the 1667 rebuilding act insisted that all buildings of any size must be made from stone or brick, this combined with the change in building shape (no overhangs) combined with the "declaring what streets and streight and narrow passages within the City of London and Liberties thereof, burnt down in the late dismall Fire, shall be enlarged and made wider, and to what proportion" mentioned in 1667's Act of Common Council re. Street Widening, meant that fires were not as quick to spread as they had been prior to 1666.

Despite all of the Garrioch argues that 1666 was indeed a turning point in fire safety and that far more large fires happened afye 1666 than before. (Southwark 1667, 1676, 1681, 1698. Shadwell 1673, Wapping 1682, Whitehall Palace, 1698, Thames Street 1682, )

He goes on to state that the fire standards of the medieval period were far better and the huge influx of people in the 17th century led to a decline in these standards and the beginning of a series of fire.

I wish I could give you a better answer and I hope this isn't an unacceptable answer that gets removed. Sources that I would recommend and would have utilised if I had access:

Dickson, The Sun Insurance Office,

Wright, Insurance fire brigades, 1680–1929: the birth of the fire service

Pearson, Insuring the Industrial Revolution: fire insurance in Great Britain, 1700–1850

Keene, Fire in London: destruction and reconstruction

Porter, The Great Fire of London