you need one statement for the last 12 months (which usually takes a week if with BKK bank) and then another statement detailing all the FTTs from the previous statement(which they usually need 1 day to do)
The OP was also seeming to infer that there's some special treatment from the UK Passport office if you use an agent which is simply wrong. Not the same situation using an agent for Thai immigration
If you can't manage to copy your passport or driving licence as proof of address, it must be a real struggle renewing your visa. As i understand, the passport doesn't have to be collected in person which saves one. For people like yourself living in far flung corners of Thailand, it's understandable if you use an agent rather than travel to CM or BKK but the OP seems to be resident in Pattaya which isn't such an inaccessible location compared to yourself
Just to be clear, not one of these agents can make the process any quicker. If applying for a new passport , the application process requires nothing more than filling in your name address date of birth etc and providing a photo with a payment. That's it. If you need an agent for that, how on earth do you manage to go to the bathroom on your own?