The chief executive of NHS England has contradicted government claims that the health service is getting more funding than it asked for.
Simon Stevens told MPs this was “stretching it” and there were “clearly substantial funding pressures”.
And, in clashes with Labour leader Jeremy Corbyn, the PM called claims of a “humanitarian crisis” in the NHS “irresponsible” and “overblown”.
But Mr Corbyn said Theresa May was “in denial” over the situation.
There have been several warnings in recent days about the pressure on the health service in England.
The Royal College of Nursing said its members were reporting the worst conditions they had experienced.
In a separate move, 50 leading doctors have warned the prime minster in a letter that lives are being put at risk because of mounting pressures on the NHS – and charities working with elderly people said long-term solutions were needed.
On Sunday, Mrs May told Sky News that, when the government had asked the NHS what it needed for the next five years, it had been given “more funding” than “required”.
But, appearing before the Public Accounts Committee, which monitors government spending, Mr Stevens said it was wrong to say “we’ll be getting more than we asked for”.
Ministers said NHS England had asked for £8bn and been allocated £10bn. But Mr Stevens told MPs that was to cover six years rather than the five-year plan he had put forward.
“I don’t think that’s the same as saying we are getting more than we asked for over five years.”
He also told the cross-party committee: “In the here and now, there are very real pressures. Over the next three years funding is going to be highly constrained and in 2018-19, as I’ve previously said in October, real-terms NHS spending per person in England is going to go down, 10 years after Lehman Brothers and austerity began.
“We all understand why that is, but let’s not pretend that that’s not placing huge pressure on the service.”
During Prime Minister’s Questions earlier, Mr Corbyn said the prime minister “seems to be in some degree of denial”, saying she “won’t listen to professionals”.
He added that Mrs May’s “shared society” vision, outlined in a speech earlier this week, could mean “more people sharing hospital corridors on trolleys”.
But Mrs May said there was always greater pressure during the winter, with the UK’s ageing population and “growing complex needs” creating extra strain.
She said claims from the Red Cross of a “humanitarian crisis” in the NHS were “irresponsible and overblown” – the only way the NHS could be funded was with a strong economy. “The last thing the NHS needs is a cheque from Labour that bounces,” she added.
She agreed to meet a cross-party group of MPs calling for politicians to put aside differences and draw up an NHS “convention” to secure its long-term future.
The latest calls for government action come a day after documents leaked to the BBC showed record numbers of patients were facing long waits in A&Es in England. Nearly a quarter of patients waited longer than four hours in emergency wards last week, with just one hospital hitting its target, according to the data.
Since the start of December, hospitals have seen only 82.3% of patients who attended A&E within four hours – the worst performance since the target was introduced in 2004.
Janet Davies, chief executive of the Royal College of Nursing (RCN), said she had heard from front-line nurses who wanted to give the best care they could to their patients but were told to discharge them before they were fit just to free up beds.
And the Royal College of Physicians (RCP) called for urgent investment to help “over-full hospitals with too few qualified staff”.
RCP president Prof Jane Dacre said: “Our members tell me it is the worst it has ever been in terms of patients coming in during a 24-hour period and numbers of patients coming in when there are no beds to put them in.”
Mark Porter, chairman of the British Medical Association’s council, accused the government of “wilfully ignoring the scale of the crisis in our NHS”. He added: “Trying to play down the pressure that services are under shows the prime minister is out of touch with patients and front-line staff who are working flat out under impossible circumstances.”
But a Department of Health spokesman said the NHS in England had 3,100 more nurses and 1,600 more doctors than a year ago. “We’re also joining up health and social care for the first time,” he added, “and investing £10bn to fund the NHS’s own plan to transform services and relieve pressure on hospitals.”
And, in a separate debate in the Commons, Liberal Democrat former Health Minister Norman Lamb asked Health Secretary Jeremy Hunt: “Is it conceivable that some of the people who are currently within the A&E target will at some stage fall outside the A&E target in the future?”
Mr Hunt replied: “I am committed to people using A&Es falling within the four-hour target.
“But I also think we need to be much more effective at diverting people who don’t need to go to A&Es to other places, as is happening in Wales, as is happening in Scotland, and as frankly is the only sensible thing.”