RE: If they don’t like working for the gov, can they still set up a private practice if they choose?
I asked the same questions to our Canadian friends. The answer in Canada is essentially “no” ( otherwise, why do people bother to come to the USA to get the treatment they need if they don;t want to wait? ).
I am not sure what the answer to the question is in the UK...
Very definitely yes. In fact many doctors practise both privately and for the NHS. Their ability to do so has been a constant since the NHS started in 1948 - it was one of the concessions the British Medical Association (doctors' professional body) extracted from Nye Bevan, the Health Minister, to secure their cooperation with the new service. For the first 30 years of the NHS private practice was small, but it has expanded significantly in recent decades.