Britain was never in a position to colonise China. For all the superficial similarities to India- an Imperial dynasty on the wane, initial British coastal concessions, divided elites- China in the nineteenth century was far harder to make inroads into than India in the eighteenth.
For one thing, by the time that the Qing had actually begun to seriously rot, there were plenty of other Western powers with a vested interest in making sure that China didn't fall into any one power's lap- be it Russia, Britain, France, or Japan.
Besides which, what would Britain gain from direct rule over China that it couldn't get from its desired state of affairs- a modernising Qing empire dependent on finance and expertise from the City of London?
The British wanted their naval bases, yes- but having got them, they ended up alongside the US attempting to keep China from being carved up. They'd gain less from direct rule over even a large chunk of China than they would from informal empire over the whole.