If you want a cheap flight from Cambridge to Taipei, you've got one airlines to choose from.
Make sure you use the search options above to search for flights to other airports in Taipei, not just Taipei Taiwan Taoyuan International (Chiang Kai Shek International) Airport. The more options you look at, the better your chance of finding a cheap deal. Just so you know, the flight typically takes 42 hrs 35 mins.
There are about five flights via Taipei every week, so you have plenty of options.
If you're planning on going to Taipei during this time, you could take a look at other airport options. Or you could try to get a last-minute bargain.