Maybe it depends on the Immigration Officer, but I've only ever had one TM30 filed at CW, despite having numerous trips within Thailand and annual extensions since then.
You'll need to present the old passport at BKK airport when you arrive so that the IO sees the Extension stamp and Re-entry permit. He will then refer to this when he stamps your new passport. Take both passports when you go to your Immigration Office to get the Extension transferred. I've done it before, and it was straightforward. They don't transfer the Re-entry permit; you have to do this at a different desk (free).
Actually the letter is only required if you get a new passport in Thailand. If you get a new passport in the UK it will be stamped when you arrive in Thailand, so won't be blank when you take it to Immigration to get your Extension transferred.