As George says - population has nothing to do with the way it works, and the UK population is 65 million by the way. There is governance at local level as well as national level.
All doctors working within the hospital sector of the NHS receive a salary - just like any other member of NHS staff - and there are set pay scales for the various grades.
General practice is a bit different and there are two forms of remuneration there. Some GPs set up and run a practice (office to you) in a similar way to the USA. Some may share the costs with another "share holder". They then receive funding from the government to take NHS patients - their services are "purchased". Out of that "salary" they have to pay the costs of running the practice: the building, other staff they employ and so on. They can also employ doctors within that set up and these doctors receive a fixed salary and have no responsibility for the costs of running the practice.
The GPs are also reimbursed in relation to the patients they care for: a fixed amount is paid per head for patients in various age groups to cover the costs associated with providing the service. This is paid irrespective of whether a patient registered on the practice list goes to the doctor multiple times per year or never crosses the threshold. Every person in the UK is entitled to be registered with a practice although in some places there is no choice as to which practice. Where there IS a choice you make that decision and register with the practice of your choice - usually it has to be one within a reasonable distance of your home and you can only normally register with one practice and that is the practice that is paid to provide your care. It is possible to change practice however if you prefer to go to another and they will accept you.
There are also walk-in clinics and minor injuries units you may go to without being registered there for care.
Hospitals also receive funding on a similar basis depending onthe number of beds and the services offered. A hospital providing transplantation or cancer care (for example) will receive some extra to cover the immense costs there for example but otherwise they must budget to cover all costs incurred.
In order to access specialist care you must be referred by a GP. Almost all specialists work within hospitals both for out-patient and in-patient care.
There are also doctors who work privately, some of them work in the NHS and also see private patients. Sometimes you can see a doctor privately and he will then transfer your care to his NHS list where the care does not cost you at point if receipt. Some doctors work purely privately - in exactly the same way as the USA.
There are downsides to the NHS obviously - there isn't a bottomless pot of money. But no one who is ill is left with no cover - if you are employed you and your employer pay contributions to the social services fund. If you become unemployed you are caught by the social services net as you are credited as having paid contributions when you register as unemployed. This covers far more than just medical care though - entitlement to medical care is based on residency. If you are resident in the UK, then you are entitled to care whether you work or not. There are some things that aren't available on the NHS but basically all emergency care needed is covered - from cancer care to accident trauma. And the unemployed down and out is entitled to the same care on the NHS as the company director who chooses to use the NHS on principle. There is no rationing policy because you come under "medicaid". If you need treatment you get it without question - with a few exceptions for very expensive drugs that are only partly funded and special permission is required for the funding. But if you need a drug or an operation or other therapy you get it immediately as required - no contacting the insurance companyfirst to get approval.
Anyone who has the money can opt for private care which they can pay for themselves or they can take out a private health insurance plan. So if you want that - it is no different from the USA. The people with money can have the frills, everyone else gets outstanding care - free at point of service. You can have doctors who are not very good in some way or another - but that can happen in the USA or any other private system too. And we can ask for a second opinion - at no extra cost to us.
There are flaws but generally the NHS is seen as one of the best health services in the world - both in what they offer and also in obtaining value for money.
I, by the way, don't live in the UK now. The system here is similar, just much smaller.