Prime Minister Rishi Sunak has repeatedly refused to say whether he uses private healthcare, insisting it is “not really relevant”.
Mr Sunak told the BBC’s Sunday with Laura Kuenssberg programme that his healthcare was “a personal choice”.
Nursing union leader Pat Cullen said the PM “needed to come clean as a public servant”.
And when asked the same question, shadow health secretary Wes Streeting said he did not use private healthcare.
In the interview, Laura Kuenssberg suggested there was huge public interest in Mr Sunak’s decisions and that former Conservative prime minister Margaret Thatcher was open about her choice to use a private GP.
Mr Sunak said healthcare was “something that is private”, adding he “grew up in an NHS family”, with a dad who was GP, and a mum who was a pharmacist.
But when pressed again, Mr Sunak did not answer the question and instead said, in general, “we should be making use of the independent sector” so patients could choose where they have treatment.
A newspaper report in November last year suggested Mr Sunak was registered with a private GP practice that charged £250 for a half-hour consultation.
Ms Cullen, the general secretary of the Royal College of Nursing, said public servants “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,” she said.
Mr Streeting said the PM’s answer to the question about his healthcare showed him to be someone who did not understand the biggest crisis in the NHS history.
He said private healthcare created a two-tier system, but patients were free to make their own choices about treatment.
Mr Sunak was interviewed as senior doctors warn of a NHS on a knife edge, with health workers striking over pay and some hospitals in crisis.
A sharp rise in Covid-19 and flu admissions in recent weeks has put pressure on hospitals, which are also dealing with a backlog of treatment that built up during the pandemic.
A&E waits and ambulance delays are at their worst levels on record.
In Sunday’s interview, Mr Sunak acknowledged the NHS was “undeniably under enormous pressure”.
When asked if the NHS was “in crisis”, he said while recovering from the pandemic “was going to be tough”, he was optimistic “we can get to grips with this problem”.
Bringing down NHS waiting lists was one of the five pledges he made in his new year’s speech earlier this week.