The number of patients on hospital wards in England has been at unsafe levels at nine out of 10 NHS trusts this winter, BBC analysis shows.
To minimise the risk of infections and delays in getting treatment, hospitals are meant to have no more than 85% of beds occupied.
But the analysis showed 137 out of 152 hospital trusts have been above that level since the start of December.
NHS bosses said hospitals had major problems discharging frail patients.
One experienced hospital boss described some of the weeks this winter as the "worst" he had seen in his career.
Meanwhile, patients have been contacting the BBC to report the chaos they have experienced in overcrowded hospitals, including long waits for treatment and operations being cancelled at the last minute.
'My mum's undignified death'
Richard Taylor, 55, from Liverpool, says he was left devastated after watching the "undignified" death of his mum Sheila in January.
She had cancer, but her local cancer centre was full and so was unable to give her end-of-life care.
She was taken to Aintree Hospital but spent 13 hours on a trolley waiting for a bed before being admitted. A week later she died at the age of 78.
"The nursing staff were fantastic, but there is only so much they can do," Mr Taylor said.
"It was awful watching someone die in this extremely undignified way. If she was an animal, they would have put her down - she was starving and dehydrated.
"The NHS is a great thing, but it is under the hammer."
The findings have been highlighted as the BBC launches a special week of coverage about the state of the NHS.
A poll by Ipsos MORI of 1,033 adults for the BBC has suggested three-quarters want to see charges increased for people coming from abroad as a way of raising more money for the NHS. Some 40% would support a rise in income tax and 37% backed charging for some services.
It comes as the government in England has announced that from April this year foreign patients could be refused operations unless they cover their costs.
Hospitals will be expected to check upfront whether an individual is eligible for free non-urgent care by asking for ID.
Bed shortages 'extremely worrying'
Chris Hopson, chief executive of NHS Providers, which represents hospitals, said the bed shortages were "extremely worrying".
The 85% occupancy mark is an internationally recognised level that hospitals are advised to stick to in order to help them manage the risk of infections and to enable them to have the spare capacity to deal with major on-the-day emergencies.
Mr Hopson said: "Above 85% and the risks start rising and once you get into the 90% it is significant. You don't get this in other countries and it just shows the pressure hospitals are under."
The analysis, which looked at week day occupancy from 1 December to 22 January, showed that over 60 hospital trusts had rates of above 95%.
One of those was Basildon and Thurrock. Its interim managing director, Tom Abell, said it had been an "exceptionally busy" winter.
He said the bed shortage was also to do with the numbers coming into hospital as well as the problems discharging patients.
"Previously it would be unusual to see more than 350 people in our A&E in one day but this is now the norm. We've had several days where more than 450 people were treated."
Andrew Foster, who runs three hospitals for the Wrightington, Wigan and Leigh NHS Trust, said the start to the year has been "the worst I've known".
"It started from Boxing Day onwards," he said. "Cubicles in A&E were full, we had ambulance staff queuing in the corridors and we could not get patients out of hospital. The whole system backed up."
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A spokesman for NHS England acknowledged the situation was impacting on the way hospitals were performing.
He said "the single most helpful change" would be to tackle the problem of delayed discharges, which is caused by a lack of available services in the community to take care of frail patients when their medical care had finished.
Without that support being provided - either from council care teams or district nursing - these patients cannot be discharged.
None of the other UK nations could provide the BBC with bed occupancy data this winter.
Analysis by Ransome Mpini and John Walton
NHS Health Check
A week of coverage by BBC News examining the state of the NHS across the UK as it comes under intense pressure during its busiest time of the year.