@Sarah **************
well the METV can only be obtained from a consulate in your home country (or one where you have a legal right of residence), so you'd have to be in the UK for that. The DTV can be applied for at most consulates around the world, a very few will only process it for residents but most allow anyone to apply. Where would be quickest for you is going to depend on where you are. If you're already in Thailand then Taipei is currently the quickest, apply one day get back the next, but you'd have to get there by the 27th as after that they move to the evisa system and most places are 10 day processing time for that.