Waits in A&E during December in England were the worst since the target was introduced in 2004, figures show.
Just 85.1% of patients were seen in four hours – well below the 95% target – equating to over 300,000 patients waiting longer than they should.
It comes as hospital bosses say they have run out of beds and cannot cope.
Reports have emerged since Christmas of patients being left for hours on trolleys in corridors and stuck in ambulances as A&E teams struggle.
Chris Hopson, of NHS Providers, said hospitals were unsafe and over-crowded, and the NHS was at a “watershed moment”, requiring long-term funding.
But ministers say plans are in place to help the health service cope, despite mounting evidence of growing pressures.
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Last week the BBC reported that thousands of ambulances had been left stuck outside accident and emergency departments over the winter because there were no staff available to receive their patients.
Inside A&E, patients have complained of being left in waiting rooms and corridors for hours as staff struggle to free up beds.
Latest figures show that over 90% of hospitals in England have too few beds available to provide safe care.
The rest of the UK is also struggling. Waits in Scotland’s major units hit their worst levels at the end of December.
The Welsh government said the health service was facing “significant pressure” and in Northern Ireland the Antrim Area Hospital has had to bring in St John Ambulance volunteers to help with a surge in demand.
‘There was no dignity – it was chaos’
Rosie Dawson, 37, is just one of the patients who has been caught up in the problems.
She was taken to Torbay General A&E on 3 January with a gynaecological problem which had left her with severe pain and bleeding.
She said it was chaos, with trolleys everywhere, staff running up and down corridors and queues of ambulances outside.
Staff could not find a private area for her to be assessed in so she ended up being examined in front of other patients.
“There was no dignity. It was degrading,” she said. “I couldn’t fault the staff, there was nothing they could do. It was chaos.”
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Speaking to BBC Radio 4’s Today programme, Mr Hopson said last year was “the first time ever” in NHS history that all of its key targets for A&E, cancer and planned operations across the UK had been missed.
He said hospitals were short of 10,000-15,000 beds and it was time for the government to decide how to fund the NHS in the long term.
“We have reached a watershed moment where either we fund the NHS to the extent that is needed to meet those standards or, and this is absolutely not what we want, we abandon those standards.
“But it is a watershed moment. We are now at the point where we can not deliver the NHS constitutional standards without a long-term funding settlement.”
Mr Hopson said mild weather and low flu rates had helped hospitals “scrape by” during previous winters.
“Maybe if we had been lucky again this year we could, just about, have coped,” he added.
“But it has not turned out that way. Flu is rising, there is more respiratory illness and the cold weather is taking its toll.”
Since 2010 the budget has been rising at about 1% a year on average whereas traditionally the NHS got over 4%.
A spokesman for the Department of Health and Social Care in England acknowledged there were problems.
He said: “We know there is a great deal of pressure in A&E departments and that flu rates are going up, and we are grateful to all NHS staff for their incredible work in challenging circumstances.”
But he added that plans were in place to help, including extra money for council-run care services so people could be moved out of hospital more quickly and the single biggest expansion in doctoring training places in the history of the NHS – 25% in the coming years.
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