In Ireland we have a two tier system.
People are entitled to free health care if they earn less than 36€K and have to wait for treatment in a public hospital. They have free GP visits and free scripts. Everyone over 70 has free GP visits, but further treatment is means tested / paid for by insurance.
If you have no health insurance and earn more than 35€K you have to settle your account yourself in full before you leave the hospital/ GP surgery for all treatment and accommodation costs.
And if you earn more than 36€K you have health insurance to cover 75% of the costs in the private or public clinic, but pay about 1€K a year premium.
The treatment is the same in public or private clinics and doctors see patients in both place. Doctors in Ireland earn hundreds of thousands a year, and it's very difficult to get into medical school here, and consultant jobs are difficult to get unless you've been through the Irish education and medical system.
Pregnant women are treated under the mother and child scheme where all services are offered free in the public area of the maternity or the maternity wing of the general hospital. If you want a particular obstetrician, you pay about 3€K, plus accommodation costs, or have health insurance. Community midwife schemes are free, but its strict to be accepted onto this home birth scheme.
Dental care is separate, but if you're on 36€K or less there are public dental clinics with waiting lists and an enmergency hospital. Dental insurance is available, but you are entitled to one visit every two years and a hygienist visit once every two years if you have paid your pay related social insurance. Pregnant women are entitled to a free dental check up, regardless of their means.
Orthodontics are available but privately paid for unless you are assessed to need them as a child, and then there are only fixed appliances available with long waiting lists. No adult orthodontist treatment is offered free.
It works ok until there are a lot of people sick at the same time and there is a Norovirus. There were 350 people waiting on trollies in AnE in Ireland last week.
Mostly everyone has a GP and people don't go to the AnE instead, as you can walk in with 60€ and be seen, or wait and be seen that day.
I cannot see how the NHS can survive post brexit, unless it makes health insurance obligatory for those who earn more than the minimum industrial wage, and free treatment is strictly means tested.