Greetings! Questions similar to this one have popped up on AH before, and as such this response is an adaptation of several previous comments I have made in the past about the various reasons why the European powers in general (including Britain) did not "colonise" more of the Qing Empire. Note that what is contained herein is more of a Eurocentric view, in that it takes the position of the European governments rather than the perspective of the Qing. For more on how the Imperial government viewed these intrusions into their lands by the "foreign devils", u/EnclavedMicrostate has written excellent responses to that end, four of which I have linked at the end. With those perambulatory notes out of the way, let us begin.

Note: along the way, I shall also be addressing several misconceptions which OP has pointed out in their explanation of the question, so do look out for those.

The British in China

"It is not the intention of Her Majesty's Government to undertake any land operations in the interior of the country"

- George William Frederick Villiers, 4th Earl of Clarendon, to Lord Elgin, 1857.

The above sentiment is once which the British, alongside most of the other European powers who would join them in the region, stuck to rather closely. The First Opium War had enabled Britain to secure consular enclaves and extraterritorial rights which the Qing government were forced to agree to (practically at gunpoint). Why they did not then go any further is an interesting question to ponder. After the Treaty of Nanking (1842), the Royal Navy maintained no less than 30 to 40 gunboats in the region to patrol the coasts and rivers against pirates, anti-foreign disturbances, and uncooperative officials. Clearly, the British did have the ability to subjugate the Qing government by force if it needed to, so why did it not capitalise upon this opportunity?

We must first consider the fact that Qing China served a different purpose in the eyes of British merchants and the government in London: a source of commercial revenue. Where "gunboat diplomacy" had opened the doors of China to British trade, it also kept those doors open. China was seen not as a potential source of "direct trade" with the rest of the Empire, but rather as an offshoot, if you will, of the British-India trade. India (the British Raj after 1859) provided the goods to trade with the Qing, as historian John Darwin elaborates below:

"It was India that provided the available means to secure British claims [in China], and India that had a big interest in doing so. British trade in China was largely an outgrowth of the India trade: 'East India' merchants sent Indian opium and cotton to China to buy tea and silk. But the opium itself was a government monopoly, and the revenue from it made up nearly one-fifth of the Indian government's income."

Even after the Second Opium War, British economic interests struggled to penetrate into the interior of the Qing Empire. Where they controlled the trade was the coastal areas, with firms such as Jardine Matheson, Dent's, and Butterfield & Swire. The shipping lines of Jardine Matheson and Swires in particular ('Ewo' and 'Taikoo' respectively) were the main spearheads of British commercial services in China. The inland trade was still anathema to the government consuls, who bemoaned any merchants that attempted to set up residence inland. These residences would overburden their administrative duties, it was argued, a sentiment which Whitehall almost fully endorsed. Darwin also remarks here on a critical point that leads into our next section of the response:

"Behind the barriers of its language and its complex currency system, and without Western-style banks or commercial property law, China was 'singularly successful at checking foreign economic penetration', remarks a modern authority."

We shall pick up this specific narrative with the British Empire in a bit, but now let us turn to the wider picture of European ventures in the Qing Empire, and why they also found inland penetration (and hence colonisation) somewhat of a puzzle.

Part 1 of 3

Hey there,

Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.

If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!