The NHS is currently underfunded, just now the government in charge would love to abolish the NHS purely for ideological reasons. Since the global recession, politics in the UK has been fought over the issues of, public spending cuts, cost of living, the welfare state, immigration; the NHS has been shunned to the side and because of this has allowed funding to minimized. A (phony) promise was made by the government back in 2009 to protect NHS spending, an increase in spending was in fact claimed but the truth is polarising.
It's privatisation in the back door, under fund it, make it under perform, all of a sudden privatisation becomes an easy argument to make.