It is likely to take a month from start to finish. You can do it yourself and take all the documents to VfS Global (and collect the new passport from them) or you can appoint a third party to do it for you.The instructions above are quite clear but supplying evidence of your address in Thailand is not easy for some.
Great at Don Muaeng yesterday, all double desks manned and virtually no queues. Through in 5 mins. Also a much better queueing system than last year's shambles and had staff checking that TM6 forms were completed before letting you into the immigration area.
Anyone just using a Thai passport requires a visa. As said, check in with British passport, exit Thailand on Thai passport, enter U.K. on British passport and exit on same. Enter Thailand on Thai passport.