If you want a cheap flight from Birmingham to Taipei, you've got zero airlines to choose from.
You can use the filters on your search to see more flights and find cheaper rates – Taipei has more than one airport. So if you don't need to fly into Taipei Songshan (Sung Shan) Airport, it's worth checking your other options.
During this peak season, accommodation prices often increase too, so it's best to book early. Or you could keep your fingers crossed and hold out for a last-minute deal.