How to hate the public health system in 10 easy steps

United Kingdom. You need to register for a GP, buy you're foreign so you're not quite sure about the process. You check the golden source: the Internet. This is how it goes.

1. Find the website of the NHS, the public health body. A fairly nice website I must say, well structured. Go to the section "Find a GP"
2. Introduce your postcode to get results near you and check the options that apply. In my case: practitioners that accept appointments at 8am and practitioners that provide travel vaccines. Get one promising result.
3. Read carefully the procedure to apply. There is a form on-line that needs to be printed and filled, nothing else seems necessary.
4. Go early in the morning to the practitioner and hand the paper. The practitioner rejects the form claiming that they use their own ones (even though mine is from the official NHS website). Also they request proof of address.
5. Back home to pick a bank statement as proof of address. Back to the practitioner, provide papers. The clerk discusses for 10 minutes with her colleagues whether they know my address and whether they should accept me. They look in a map and affirm that there's another one closer to my house and advise me to register in that one.
6. In reply, I indicate that I know of the existence of the other practitioner, but I came specifically to this one due to the timetable and the travel vaccines (not provided in the other one). They indicate that travel vaccines are only provided after being registered for 6 months, hence I'll have to go private and pay out of my pocket.
7. Accepting that major drawback (the vaccine is the only reason for which I was registering) I decide go register anyway, you never know. The "local" form that I'm requested to fill looks exactly the same as the one I brought. After filling the form, the clerk uses it to type the details on a computer, it makes me wonder what difference it made if the damn thing is to go on a computer.
8. They claim the postcode of my precious address, EC2A 3AH, isn't valid. I need to bring up Google Maps in my phone to prove them wrong; it makes me worry about the core competences of a bunch of people who can't even read postcodes.
9. After typing in data clerk announces I need an introductory appointment and mentions Wednesday at 4:40pm, I request any day at 8am. "We don't arrange any appointments before 9am". I indicate that according to the official NHS website they do, which is one of the reasons I chose this practitioner. "I don't know anything about that website, but we don't arrange appointments before 9am". It makes me worry that an NHS employee doesn't know about the official NHS website nor its contents.
10. I lose faith in the process and ask the clerk to cancel the registration, I will register somewhere else. Reply is the registration is now effective and cannot be cancelled easily, it will take some weeks to de-register. Weeks, they say. I give up and simply leave.

If this is what my tax goes to I'd rather have the NHS completely shut down.