nhs.uk/conditions/coronavir...
It looks like it's much easier to book your vaccine now:
The 3rd dose is for people who had a severely weakened immune system when they received their 1st or 2nd dose.
The vaccine may not have given them as much protection as it can for people who did not have a severely weakened immune system.
If you've had a 3rd dose for people with a severely weakened immune system, you'll be eligible for a booster (4th dose) from 3 months (91 days) after your 3rd dose. You cannot book boosters (4th doses) using this service yet, but your GP or hospital specialist will invite you when it's due.
Will you be able to bring one of the following things to your appointment?
You need to bring one of these things to show that you had a severely weakened immune system when you had your 1st or 2nd dose:
a referral letter from a GP or hospital specialist telling you to get a 3rd dose
a hospital letter that describes the condition or treatment that caused you to have a severely weakened immune system
a prescription or a medicine box with your name and the date showing when the medicine was prescribed - this must show that you had a severely weakened immune system when you had your 1st or 2nd dose
A clinician at the site will check your evidence to make sure you get a suitable dose.
I don't have a specific invite, but I was able to continue through to booking an appointment.