Unlike the US, Canada or Japan, the UK doesn't have a substantial Taiwanese community. However, at least three Taiwanese living in Britain have made a splash in their fields. They are:
Ching-He Huang (b1978, 黃瀞億) is a food writer who's gone on to present TV cookery shows. At age five her family emigrated to South Africa; six years later they moved to the UK. I interviewed her by email for this article.
Hsiao-Hung Pai (b1968, 白曉紅) is a campaigning journalist who has written for The Guardian and various other publications. I interviewed her and wrote about her first book, Chinese Whispers, for Taiwan Today, an English-language government website.
Richard Lin (1933-2012, 林壽宇) is best known for his modernist painting, one of which was sold by Sotherbys in 2008 for GBP34,850. Since the 1980s he's devoted himself to sculpture and spent more time in Taiwan than the UK. He first travelled to the UK in 1954 to study architecture and art, and then spent decades in London. He's a descendant of the rich and once-powerful Lin family of Wufeng, Taichung.
Although she's now based in Macau, Chu Mei-feng (b1966, 璩美鳳) - who lived for a time in London - is also worth mentioning. I'm guessing this former politician relocated to the UK to find peace and obscurity, having acquired more than enough fame and notoriety in Taiwan as a result of one of the country's most spectacular sex scandals.