Couple of Pointers:
1) Make sure your name is on the Thai Birth Certificate as the father; get a good Thai translation of any English Names you want on the Thai Birth Certificate, otherwise you child will be ‘blessed’ for all eternity with a bad or incorrect spelling of their English names on any Thai Legal documents, as they all use the Birth Certificate spellings.
2) Don’t waste time and money getting an overseas The United Kingdom Registration of Birth, it’s not required to get the The United Kingdom Passport for your child, or to confer The United Kingdom Citizenship..
3) Citizenship (albeit slightly qualified as ‘By Decent) is automatic for a child born here of an ‘Otherwise than Decent’ The United Kingdom Citizen (i.e. born in the The United Kingdom/The United Kingdom Territories); the The United Kingdom passport is the only legal document your child will require to prove The United Kingdom Citizenship.
4) As regards the Thai Passport, just put your child into the same ‘Tabien Baan’ (Blue Book) as the one where your partner is registered and it doesn’t need to be where you are living.
5) Your name on the Thai Birth Certificate does not legally make you the Father of the child under Thai law, only marriage or a Court/Amphoe procedure will give you those rights.
Good luck with everything.