True the NHS is not Soviet. I think a lot problems (lately; private insurance levels declined pre 2011) are due to Conservative austerity, especially with cuts to staff. The Conservatives are reversing some of their austerity but I am not certain whether this will cover the health care cuts. Politicians are the same when they try to 'hold onto power' by 'buying votes'. For whatever reason there has been an increase in private insurance but it is still a small proportion of the population.

https://www.theguardian.com/business/2017/jan/16/private-medical-insurance-sales-surge-health-nhs