Hmm, here's some examples from a simple search, starting with my own thread on the subject (and it's one of those subjects that occasionally crosses my mind with "I should try something like it one of these days"):
https://www.alternatehistory.com/forum/threads/a-british-formosa-a-thought-exercise.262646/
More recently, we have the following threads:
https://www.alternatehistory.com/forum/threads/british-taiwan-formosa.427217/
https://www.alternatehistory.com/fo...onquer-a-surviving-kingdom-of-formosa.452185/
However, what you're asking for is a different kettle of fish, since it's passing directly from Dutch control to British control without any Chinese intermediary (that is, no Ming loyalists/Koxinga trying to set up shop after being overthrown by the Manchus) except via immigration. In that case, there's no need to have Formosa ceded in perpetuity from Beijing because it was never part of China in the first place. China only gained interest in Formosa precisely because of the Ming loyalists setting up shop across the Taiwan Strait and hence making the Manchus nervous about rebels setting up shop too close to the Empire and thus posing a security risk. The end result of early British colonization of Formosa would be a completely different history of the island, which absent the Hokkien-speaking factor would be more similar to SE Asian history in general and in particular sharpening the Anglo-Spanish rivalry (because the Spanish still own the Philippines in this scenario). In that case, Britain would still want to trade with China, and hence with Guangzhou still the only port through which foreigners would trade with the Chinese, the British would probably still want something similar to, if not exactly, Hong Kong as long as it's on the Pearl River Delta and near Guangzhou. However, in this case there's another alternative way for the British to trade with China that would bypass Guangzhou completely, and that would be to get as close to Xiamen (Amoy) as possible. Taiwanese is basically a transplanted version of Southern Min (and in this case heavily influenced by Western languages - Dutch, Spanish, and English - as well as Aboriginal languages), and the prestige speech of Tainan is similar to the prestige dialect of Southern Min in general, which is based on the speech of Xiamen (and before that Quanzhou was the representative prestige accent, whose Taiwanese cousins are all over the island, primarily in coastal areas). Given that at this early stage in the 1600s or so many would still have close relations with Fujian across the Straits and Fujianese immigrants came to Taiwan despite the bans on emigration by the Qing dynasty, in this case Britain would want Xiamen as a treaty port, in which case Hong Kong/Guangzhou is unnecessary from a British POV; Quemoy (Jinmen/Kinmen) and Wuqiu, however,
would be seen by the British as necessary due to proximity to Xiamen (Amoy) and Quanzhou (Chinchew). And that's just the beginning.