Immigration requires a letter of verification from the British Embassy before they will transfer my visa/extension into my new passport. Anybody know how one is obtained and are they going to charge me a stupid fee for the pleasure?

You go to the Embassy with your old and new passports and they will do the letter while you wait, they don't charge a fee.

If you don't live in Bangkok, I think you can do it by post.

For other immigration offices it's worth checking their requirements to save a wasted journey to the embassy. For example Khon Kaen don't require a letter.