Upvote:7
I am aware that the British didn't have enough manpower to hold such a vast territory with such a large population, so Britain would not be able to topple the Qing Dynasty completely and set up another British colony
You answered it yourself:
The UK wasn't always looking for new territories. There were both a colonial and an anti-colonial factions in parliament. Sometimes the colonials were the majority, and sometimes the anti-colonials.
Prime minister at the time of the First Opium War was sir Robert Peel. He's remembered as the creator of modern police ('bobbies'). Sir Robert focused on domestic affairs, and was a proponent of free trade. Colonialism wasn't very high on his agenda, if at all. Colonizing China, not even remotely.
It's a myth that the UK (or any other colonizing nation) colonized whatever and whenever they could. Those countries have different political parties with different views on colonialism. Some are in favour, others firmly against. It simply depends on which party is in office.
Charles George Gordon (of Khartoum fame), for example, had the bad luck he was sent under an anti-colonial government.
Another example is the First Boer War in which Transvaal gained its independence. A pro-colonial government would never have granted it. The prime minister was Gladstone, who was [somewhat of] a liberal. Not a supporter of colonialism.