Had my 4th jab this morning, the booster after 3 primary jabs. I was a bit concerned about whether they would do it as I had my 3rd jab quite early (before the computers could record it properly). However, I was pleasantly surprised - they gave it to me without any fuss. I took all of my paperwork with me (specifically the letter I had from the time of my 3rd jab saying why I needed it) and the nurse checked briefly with the doctor supervising the vaccination center and he quickly nodded his agreement. It does seem like everyone involved is now much more aware of us, and the policies around 3rd/4th jabs.
I see a lot of people on these forums worried about whether they’ll be able to get their 4th jabs smoothly, so hopefully my experience will give you some reassurance, although clearly different areas of the country might be better/worse.
Now I’m just hoping that I start to feel a bit unwell (which I would take as a good sign that my immune system is responding to the vaccine).