How long will you be in the UK? With all the current delays in renewing passports, I'd be worried about not getting the new (and old) passport back in time for my trip home! Renewing in Thailand is relatively easy if you live near Bangkok or Chiang Mai, or are happy with making the trips to submit application and collect the new passport, or don't mind paying an agent to do this for you. You also don't submit the old passport with the application (just a copy) if you renew in Thailand.
Either way, you'll have to make a trip to Immigration to transfer Extension stamps into the new passport.