@John *********
Yes, this is the process but step 2 needs a translation service-
1. IN THE UK: Marriage certificate legalised by the FCDO in Milton Keynes (2 documents, original and legalised copy))
2. IN THE UK: Marriage Certificate AND the Apostille from the FCDO Translated (2 translations from 1., now 4 documents in total)
3. IN THE UK: Marriage Certificate AND the Apostille from the FCDO AND their translations verified by the Thai Embassy in London (4 verifications from 1. and 2. giving 8 documents in total)
4. IN THAILAND: All the above (i.e. all 4 documents & their translations, making 8 in total) Legalised by MFA in Bangkok
then register your marriage at your local Amphur.