Rishi Sunak has refused to say whether he and his family use private healthcare at a time the NHS struggles to meet demand.
The Prime Minister insisted today it was "not really relevant" whether he would be prepared to pay for faster treatment.
But the millionaire Tory leader admitted the NHS was "undeniably under enormous pressure".
Pat Cullen, Royal College of Nursing (RCN) general secretary, called for the PM "to come clean" on whether he paid for healthcare.
Asked if the health service in the UK was "in crisis", he told the BBC's Laura Kuenssberg show: "The NHS is undeniably under enormous pressure and I’ve spent today talking to NHS leaders, all day in fact."
He added: "Recovering from Covid is going to be tough and we’re seeing that play out on our TV screens every day and in communities up and down the country, but actually I came away from all my meetings today with a renewed sense of confidence and optimism that we can get to grips with this problem."
But he refused to be drawn on whether his own family relied on the NHS. He added: "As a general policy I wouldn’t ever talk about me or my family’s healthcare situation.
"But it’s not really relevant, what’s relevant is the difference I can make to the country.”
Cullen, who leads the nurses' union, said: "I think as a public servant, you ought to be clear with the public whether or not you are using private health cover.
"That’s about being open, it’s about being transparent, and it’s about honesty.
"And those are characteristics that if you were talking to the public, which I’ve done over the last while on picket lines, that are characteristics that seem to be missing at the minute.
It comes as Keir Starmer has defended backing the use of the private sector to drive down NHS waiting lists despite his leadership pledge to "end outsourcing in our NHS".
The Labour leader told Sky News: "We’re not talking about privatising the NHS. The NHS has always used elements from the private sector, GPs are an example of that."
Pressed about his pledge, Starmer replied: "Outsourcing of some issues and functions I don’t think has been very effective."
The Labour leader also warned the NHS "is on its face".
He added: "We’ve got to acknowledge that the health service is not just on its knees, it’s on its face… there are 7.2 million people on the waiting list.
"Speak to anyone who works in the NHS and they’ll tell you just how stressed it is. My wife works in the NHS so I know this first hand.”
"Just at the moment we’ve got a crisis and it’s the worst crisis we’ve ever had and that’s because we’ve had 13 years of neglect… Of course Covid put extra pressure on the NHS… but the waiting lists were 4.6 million before we went in to Covid."
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