https://www.youtube.com/watch?v=koGignAPGgs
In this vox's video, the narrator says that the Royal Family gives their crown estate (a large number of high-value real estate owned by the family around Britain) to the government and the government then gives them money in return every year. So, the royalty doesn't cost anything to the Tax Payers.
How come the Royal Family owns these estates? If British Monarchy had fallen, wouldn't these estates have already transferred to the Government of the UK? So, indirectly, it can be said that tax payers are paying for Royalty in the UK.
For e.g., Romanov owned many castles and other real-estate in Russia but after the Russian Empire fell, the Soviets took over all these lands and buildings. And it was the right thing to do because Romanov's bought these estates with people's money.
The origins of the Crown Estate go back to the Anglo-Saxon period, and quite possibly even further. A monarch, like any normal aristocrat, needs estates to provide them and their household with food. Unlike any normal aristocrat, a monarch needs to be able to go around their realm to enforce their authority. As such many early medieval courts were itinerant, travelling around the kingdom, consuming the agricultural surplus. A monarch could stay with their vassal lords, but these lords had their own households to feed, and some weren't always on great terms with their rulers. As such, it was handy to have some lands that the monarch owned personally. The Anglo-Saxons called these estates royal vills. Examples include Edwin of Northumbria's estate at Yeavering, or Alfred the Great's vill at Chippenham. As the coin economy developed rulers could use their estates to not only feed their courtiers and soldiers, but to finance them as well.
The Norman Conquest saw the appropriation of property on a massive scale. William the Conqueror took around half of the country for his personal royal demesne. Over time, this royal demesne gradually shrunk as kings granted land to younger sons and to loyal servants. Granting land was a key part of the patronage that shored up the monarch's position.
Until 1689 (apart from the brief republican gap from 1649 till 1660) the monarch was, in practice as well as theory, the executive branch of government. But after the Glorious Revolution the monarch ceased to receive the proceeds of taxation, which was henceforth controlled by Parliament, which used it primarily to fund the military. Parliament left the monarch the responsibility for funding civil aspects of government primarily from their direct income (their estates, licence fees, the postal service), but eventually these sources proved insufficient. As such, George III surrendered these sources of income upon his accession in 1760, and the aspects of government they funded, to Parliament. To ensure that the king could maintain his standard of living, Parliament granted him a fixed annuity from the Civil List, which had originated as the monarch's way of paying civil government officials. Technically, this was a temporary arrangement, and thus has been renewed by every British monarch upon their accession. Theoretically, every monarch has lent Parliament the income from the Crown lands for their lifetime.
Until 2012, the monarchy was funded by the Civil List and grants from the Department for Culture, Media and Sport and the Department for Transport. In 2012, this was replaced by the Sovereign Grant, 15% (now 25%) of the annual income of the Crown Estate, so the monarch's income is now more closely tied to the Crown estate than it has been in centuries. This has made the monarchy much richer, partly because the annual Grant is not allowed to be smaller than the previous year's.
It is important to note that the Crown Estate is merely the land that the monarch holds as the monarch, not all the land that they hold as an individual. The monarch has been the Duke of Lancaster since 1399, when the Duke of Lancaster seized the Crown. As per the arrangement with George III, the monarch retains all income from the Duchy of Lancaster. The heir to the throne is the Duke of Cornwall, and retains all income from the Duchy of Cornwall. It is important to note that these duchies are not simply the counties of Lancashire and Cornwall. English earls and dukes never actually owned their counties. They were typically the biggest landowners in the county, though the title became increasingly honourary. The Duchy of Lancaster now includes more land in Yorkshire than in Lancashire. The royal family has a number of other sources of income, such as the money people pay to visit Buckingham Palace.
Realistically, the Crown Estate is far to large for any government to make it the private property of the Windsor family, in the event of the abolition of the monarchy. The Crown Estate is the property of the Crown, not Elizabeth Windsor. While it originates as the monarch's personal estates, it ceased to be as such in 1760.