Formosa is quite a big deal as alongside Hawaii as a protectorate, the British can basically travel West or East and be comfortable for coal stations, giving them additional strategic freedom.
However, with the British there, I can see Formosa becoming incredibly powerful. Hong Kong was valuable as a way to trade, but Formosa can functionally support a navy dedicated to controlling the region and its trade. This goes beyond selling goods to China, but controlling exports from China and in theory Japan if that is seen as a worthwhile project.
The likely motivation would be to take over the trade it had with the Japanese and Dutch, and edge the Dutch out of East Asia.
This could (butterflies willing) mean a very different Opium War. The British could well have a fleet stationed on Formosa that the Qing could be cautious of, changing the diplomatic relations with them - but also meaning that a British invasion could be faster and more dangerous. It also means in the precursor that rather than traders buying from India, it could be done from Formosa itself (hell, they make a small market themselves and could even grow it in Taiwan (potentially, I'm not sure if the climate is wrong).
What is the most exciting aspect however is the potential of the British supporting the ascension of Zheng Kezang. After all Tungning saw itself as the rightful Empire of China. The Opium Wars could spill out into a major clash between an Anglo-Chinese Ming Restoration and the Qing, meaning not only the trade rights into China, but potentially large swathes of China under a Southern Ming Protectorate. That can go two major ways - massively more profits for the British and a large Chinese puppet state for a long time, or the development of Southern China as a sort of Meiji-China.