My personal recent experience with two young kids in the UK in London is that urgent care is very good. So like emergency see-someone-right-now care like sudden fevers, unexplained rashes, injuries etc. You get seen and usually quite quickly (at least for triage). My daughter was 10 weeks old in mid-2022 when she got an infection and we went to A&E (i.e. ER) and were triaged, IV'd with antibiotics, and settled into a single room (with ensuite and space for parents to sleep too) within 2 hours, then stayed for 48 hours with observation from nurses every 4 hours. Someone even offered us tea and coffee and breakfast. All for free. That is pretty good I think.
But the issue with the NHS in my opinion is the doctor/GPs. It is very difficult to get an appointment for non-urgent stuff. You have to explain to a receptionist why you need an appointment and often it is an untrained receptionist deciding if you get to see a doctor or not. If you do manage to convince the receptionist, then you are often facing a 2 or 3 week wait for the appointment, which may get cancelled or if you are lucky only be late by 2.5 hours. At our physical doctors building there are three separate clinics all duplicating the same service - there are 3 separate receptionists doing their own separate clinic and work betide you if you go to the wrong desk!
Of course as the GPs are so useless, everyone goes to the hospital to try to get seen.
These generalisations are generally unhelpful!
It’s definitely underfunded (which healthcare system isn’t?) but the rest of this is hyperbole. The UK doesn’t have one hospital.