Rishi Sunak has refused to reveal if he uses private healthcare as NHS waiting times for GPs, ambulances and hospitals soar.
The prime minister said his own healthcare arrangements are "not really relevant" as he insisted bringing down waiting times is one of his key priorities.
But the head of the Royal College of Nursing (RCN) told him to "come clean" and Labour said Mr Sunak gave the impression of a leader who "not only doesn't use the NHS but doesn't understand the scale of the challenges".
While former Conservative prime minister Margaret Thatcher said it was her "right as a free citizen to spend my own money in my own way" on private healthcare, Mr Sunak refused to say if he has.
In November, the Guardian reported Mr Sunak is registered with a private GP in West London that guarantees patients with urgent concerns are seen "on the day".
After being asked several times whether he has private healthcare on the BBC's Sunday with Laura Kuenssberg programme, he said: "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."
He said healthcare is a "personal choice" and discussing his own situation is "a distraction from what the real issue is, and the real issue is are we making sure there's high quality healthcare for the country".
"But when it comes to the private sector in general, we should be making use of the independent sector. I don't have any problem with that whatsoever," he added.
Pat Cullen, head of the RCN which is set to strike again this month, said Mr Sunak should "come clean".
"I think as a public servant, you ought to be clear with the public whether or not you are using private health cover," she told the BBC.
"That's about being open, it's about being transparent, and it's about honesty.
"I think he needed to come clean. As a public servant he is elected by the public, so he is accountable to the public, and when you're accountable to the public, you have to be honest with them."
Shadow health secretary Wes Streeting said he does not use private healthcare and said Mr Sunak was out of touch.
PM 'missing' economy boost plan
Mr Sunak has also come under fire over his five-point plan announced this week, specifically on promising to halve inflation, grow the economy and reduce debt.
Andy Haldane, the Bank of England's chief economist until June 2021, said the PM is still "missing" a plan to boost the economy.
He said there is "not really a growth programme at all" and the plan is "short that piece of the jigsaw puzzle".
"Which is, what's the plan that's going to boost growth over the medium term, enable pay to pick up, allow public services to be paid for and financed properly?" he told the BBC.
"We're still missing that."
Mr Haldane added that an "improving picture is needed in 2023" but optimism, innovation and investment "will only happen if people have some sense of a brighter tomorrow for the economy".
"That's the main reason why businesses are hiking back in investing right now, that's why the plan really matters," he added.
Mr Sunak said inflation is predicted to halve this year due to the government's autumn statement decisions and said public sector pay deals, which have caused strikes, are part of the strategy to bring down inflation.