http://www.legalisationoffice.org.uk/
https://www.gov.uk/get-document-legalised/apply-for-legalisation
Note this:
Education Certificates
Please ensure that all education certificates presented for legalisation are signed, certified and dated by a UK solicitor or notary public, or by an official of the British Council. If certified by the British Council then it must be an original educational qualification certificate, please check with your local British Council first as this service is not available at all locations.
The Legalisation Office in Milton Keynes will forward the document to the Thai Embassy in London for you, although you may have to have prepaid the postage. It too about 2 weeks for me, but I was in the UK at the time which makes it a bit easier.