I am having a lot of trouble convincing anyone.
To get fair, OP, it is very very unhelpful that the nhs website says : basically don't use this site till you've received your letter.
I can't see how anyone could be convinced this was ok/ legitimate.
Telling anyone all the instructions above:
ie you won't be able to book unless you are eligible. Just isn't convincing.
Not everyone is even getting a letter. Some get a text. Some gp's phoning.
Why the nhs website hasn't adjusted?
It's not helpful. Is it?