Thank you for posting this. I followed the procedure, and found it surprisingly easy - even though I never received an appointment letter and didn't have a login.

I followed the above link (https://www.nhsinform.scot/covid-19-vaccine/after-your-vaccine/get-a-record-of-your-coronavirus-covid-19-vaccination-status). This took me to a page where I filled in my name, date of birth and the date of my first vaccine. To my surprise, it recognised me, and gave me the option of having a vaccination certificate posted to me, or downloading a PDF. I chose the latter. I saved the PDF and also printed a copy.

The certificate contains all the details of both doses, including a 2D bar code for each dose. The bar codes apparently expire one year after you receive the certificate (regardless of the date of the vaccinations, which is slightly odd). There is no expiry date shown for the certificate itself.

So, for anyone who needs proof of vaccination, this seems to be a good way of getting it.