The Thai Embassy now requires details of your covid-19 vaccine status as part of the certificate of entry applications. From May 17th, 2021, you will be able to access your COVID-19 vaccination status through the free NHS App. https://www.nhs.uk/nhs-services/online-services/nhs-app/
You can access the app through mobile devices such as a smartphone or by tablet. Proof of your COVID-19 vaccination status will be shown within the NHS App. The Government recommends that you register with the app before booking international travel. You can also call the NHS helpline on 119 (from May 17th, 2021) and ask for a letter to be posted to you. This must be at least 5 days after you’ve completed your course of the vaccine. Expect the letter to take up to 5 days to reach you. This will also assist upon arrival in Bangkok where you may not have an internet signal to access the app and demonstrate your ‘status’ to Thai immigration.
Full details can be found here – covid-19-vaccination-status-when-travelling-abroad