I've just done my 2nd UK passport for my 11 year old. It's pretty straight forward if you read up on it. I've attached a booklet. It takes 12 weeks at present. You can apply from the UK as long as you have the relevant passport photos of correct size and documentation. You have to write a letter explaining the situation, the passport has to be sent to Bangkok for collection. Or if you are still in Thailand you can go the British Embassy and sort it there, but the application is still sent back to the UK to be made. You need his mother to write a letter of consent. I just wrote it myself and emailed it to my wife, she printed the letter out, and signed it. I then sent the letter by email back to the passport office, with a photo of my wife holding her I.D. card.
6.4824_HMPO_Overseas_Guidance_Booklet_Applying_outside_the_uk.pdf