While I certainly have a few frustrations with the NHS here and there, overall, it's been a very good experience for me.
The only extended waiting times that are a bit unreasonable I have experienced are those due to COVID. I was urgently referred to rheumatology, and the wait time is 6 weeks (for an
urgent referral - even my GP was like,
What?!). This is longer than pre-pandemic times for my area, but mainly due to the pandemic collateral damage (e.g., catching up on the huge backlog of missed appointments during the pandemic, staff being ill and not permitted to work, staff who cannot come into work due to a family member having COVID symptoms even if testing negative, and so on).
My MIL was also urgently referred to rheumatology (in a totally different location in England), and her quoted wait time was 4 weeks. She looked into paying privately to move ahead in the queue, and for a couple hundred quid, they were only able to move her appointment forward about a week. If the difference was more significant, she would have paid, but since the difference was something like 5 days, she decided to save the money and attend her NHS appointment.
In regards to my GP surgery, I've found it actually functions better since the pandemic. The introduction of virtual appointments and remote monitoring of chronic conditions has been great. Nine times out of ten, I log onto the system in the morning, and am able to book a virtual appointment the same day. And in all instances where the doctor thought I needed to be examined in person, I was given a face-to-face appointment a few hours after the virtual one.
I order repeat prescriptions online, and within 48 hours (usually within 24), they are ready at my nominated pharmacy for collection. I haven't looked into delivery, but I know my local pharmacy offers their own service. But I like to pop into the pharmacy in person to have a chat with them; they are lovely people. And right next door to my GP surgery, so bonus points.
My GP surgery has a phlebotomy department upstairs, but if the opening times aren't convenient, you can book an appointment at any of the phlebotomy departments in any of the GP surgeries or hospitals in the area - they have varying opening times to be able to suit most anyone's schedule. Just book online, show up to your selected venue, and get it done. Pre-pandemic, almost everyone just did a walk-in system which was fine, but the queues could be long. Personally, I love the appointment system so much more. In, out, and done.
You can see NHS specialists outside your area, but you may need to be assertive about it. I have found that you need to be your own advocate here, more so than in the US. It was a bit awkward at first for me (because I'm a very non-confrontational person), but I've gotten a bit more used to the system. It's not that anyone's necessarily actively against you, but there's red tape, a lot of it, and it must be obeyed. So the default approach will be to send you to your closest hospital X for treatment, unless you specify you would like to go to Y hospital further away instead.
There are pathways for some rare/super specialized stuff as well. If you need that level of care, you'll likely be referred to a tertiary hospital that can offer those specialized services - even if that hospital is not local to you.
I recommend to reach out to relevant charities if you run into problems or have any questions. Here are a selection suggested by the Royal College of Ophthalmologists:
https://www.rcophth.ac.uk/patients/charities/Also, it may be helpful to have your current doctor write a letter regarding your condition to give to your new doctor in the UK (e.g., what tests you've already had done, the results of said tests, any future tests you may need and why and when, your current treatment plan, details of previous treatment plans if they didn't work and why, and so on). I've found that some doctors in the UK like to start from scratch (do their own testing), and having a letter from your current doctor might help with that.