My son, now 16, has been living with me since he was 4 years old and was adopted formally under Thai law last year at the age of 15. Apparently the adoption is recognised under UK law, but that does not automatically entitle him to British nationality or a UK passport. Any advice from anyone else who has adopted abroad from outside the EU?
The general guidance for children born overseas, including adopted children, is here: https://www.gov.uk/government/publications/guidance-on-how-adopted-children-can-become-british/intercountry-adoption-and-british-citizenship
It is possible that he is automatically a British citizen but only if the adoption was certified as in accordance with the Hague Convention and you were resident in the UK at the time the adoption was made final.
If not, you may still be able to register him as a British citizen: https://www.gov.uk/register-british-citizen/children-born-outside-uk The full guidance is quite lengthy but particularly see pages 30 and 31 for the information you need to provide.