I am in the middle of doing this now. I have 3 of the horrible little blighters. I wasn't married when the first one was born which makes it more difficult, after 2006 I think they changed the rules so it didn't matter if you were married or not. For the bastard kid I have to fill in a "Domicile Form", which the British Embassy said they would send me but never did and attend an interview. For the other 2 which I was married when they were born it isn't really a problem. I have copied and pasted what the Embassy sent me below.
Before processing an application, Original documents are required plus one photocopy of each supporting document. All originals will be returned at the time of application. We require translations (ie official translations from a licensed translator) of any document(s) not in English. We need to see:
• Child’s official birth certificate, issued by the Thai District Office. We will follow the names as they appear on the local document.
• Documentary evidence of father and/or mother’s nationality status – UK FULL VERSION birth certificate, naturalisation or registration certificate.
• Parents’ marriage certificate
• For children born on/after 1 July 2006, it is no longer a requirement for the parents of the child to be legally married
• Evidence that any previous marriages of the parents have been dissolved – divorce or death certificate as appropriate
• Both parents’ passports
• Child’s Thai passport (if applicable)
• We need the full version birth certificate of the parent transmitting nationality (ie with both parents’ names on it). If you do not already have your (full) birth certificate, you may obtain if from the General Register Officer
http://www.gro.gov.uk/gro/content/certificates/Hope this helps
Regards
Jim