When I have used my UK debit card at a hospital in Bangkok they said their machine was giving me a choice of baht or pounds. So which should I choose to ensure the conversation to pounds takes place at the Thai end?

Always choose to be charged in the local currency.....in this case, Thai baht. If you choose pounds, you'll get a much worse exchange rate.

Edit to add: This is known as Dynamic Currency Conversion. Google that to obtain further information, if needed.

Edited March 7, 201610 yr by TheAppletons

As said all local payments should be made in baht. That "offer" was "DCC" and would provide a very poor rate of exchange and suspect your home bank would still charge as an overseas transaction and take there normal usage fee. A total rip off for customer but a money maker for banks.

Thanks. I have occasionally used the card for other purchases (I think one was tickets from ThaiTicketMajor) but there was no choice of currencies. Any idea why? Would it only apply above a certain amount, for example?

It applies by the bank being used and the company making charge - some banks do not try to force this onto customers and some business owners will automatically not use. But some others like the short term profit.