National Health Service, currently struggling with lack of personnel, but in general I have a family doctor I visit, on average, twice a year, for general check-up and follow-up. I can be recommended to a specialist if deemed necessary, with varying degrees of waitimg time.
For emergencies, I can either call a line, speak with someone and either have an ambulance sent directly to wherever I am or get directed to the nearest hospital, where they will already be expecting me.
No payments, even if I need an ambulance ride, a surgery and a few days in the hospital.
A good portion of people - mainly in large population centers - resort to private care, through health insurances, some out of pure need (pediatrics, cardiology, ob/gyn, psychology and psychiatry are specialities where long waiting lists exist) but the professionals working at the hospital are usually the same working private, due to a lack of effort from the state to make doctors exclusive to the NHS.
Private healthcare is usually faster to access and feels more luxurious but when things go very wrong you always get sent to the public hospitals. Cancer and other expensive care illnesses are sent to the NHS, which is usually the first to invest in expensive treatments to get a situation solved as quicky as possible and save time and money and free up space for the next in need.
Is it perfect? Hardly but it works. Nobody really knows or even understands how but it truly works.