The NHS is facing a “humanitarian crisis” as hospitals and ambulance services struggle to keep up with rising demand, the British Red Cross has said, following the deaths of two patients after long waits on trolleys in hospital corridors.

Worcestershire Royal hospital launched an investigation on Friday into the deaths and did not deny reports that they had occurred after long waits on trolleys in corridors over the new year period.

On Friday, doctors’ leaders said more patients could die because of the chaos engulfing the NHS.

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The deaths prompted claims that the health service was “broken”, and long waits for care, chronic bed shortages and staff shortages were leading towards what the head of Britain’s A&E doctors called “untold patient misery”.

Mike Adamson, chief executive of the British Red Cross, said his organisation was “on the front line”. He said: [We are] responding to the humanitarian crisis in our hospital and ambulance services across the country. We have been called in to support the NHS and help get people home from hospital and free up much needed beds. This means deploying our team of emergency volunteers and even calling on our partner Land Rover to lend vehicles to transport patients and get the system moving.”

It is believed that one woman died of a heart attack after waiting for 35 hours on a trolley in a corridor, and another man suffered an aneurysm while on a trolley, and could not be saved.

It is also believed that another patient was found hanged on a ward at the Worcestershire Royal hospital, which admitted that it was under serious pressure, partly as a result of the extra strain hospitals face during winter. The deaths are said to have happened between New Year’s Day and 3 January.

Many other patients who visited Worcestershire Royal hospital this week told the Guardian of long waits in A&E, corridors lined with patients, and overstretched staff doing their best to cope.

Dr Mark Holland, the president of the Society for Acute Medicine, said: “For a long time we have been saying that the NHS is on the edge. But people dying after long spells in hospital corridors shows that the NHS is now broken.

“We have got to the point where the efforts of staff to prop up the system are no longer enough to keep the system afloat. We are asking NHS staff to provide a world-class service, but with third world levels of staffing and third world levels of beds.

“That so many other hospitals in England are facing the same pressures as the one in Worcester means that other fatalities could occur. I would suggest that the same thing could happen in other hospitals, because lots of hospitals are under the same pressures.”

It is also possible that mainly frail elderly patients admitted to hospital over the festive period may have died because they received inadequate care on wards where staff were ill-equipped to deal with their conditions, Holland added.

“At the moment, we have lots of patients in the wrong beds in hospitals. That is, patients admitted as an emergency, but who do not need an operation, being looked after on wards that usually look after patients with surgical care needs,” he said.

“They may not have nurses with the right skill mix or the same level of dedicated medical cover [as general medical wards], so we know that these patients often don’t get the same level of care. Therefore I fear that during the Christmas and new year period, people in non-specialist beds may have come to harm.” Holland added that he could not estimate how many may have died as a result.

Fifty of England’s 152 NHS acute hospital trusts were forced to declare an alert last month, and sometimes temporarily scale back the level of care they offered to patients, because they could not cope with the number of people seeking medical attention, according to analysis by the Nuffield Trust health thinktank. Every hospital in Essex has had to go on “black alert” – the NHS’s highest level – in recent weeks.

In December, seven trusts had to declare the highest level of emergency 15 times, meaning they were unable to give patients comprehensive care. Paramedics have told the Guardian they have had to wait for up to eight hours at a time outside A&E units to discharge a patient into the care of hospital staff, because emergency departments cannot accept any more admissions, thereby lengthening 999 response times.

Dr Taj Hassan, the president of the Royal College of Emergency Medicine, said figures it obtained from hospitals across the UK showed some were treating as little as 50%-60% of A&E patients within four hours, far below the 95% target.

“Figures cannot account for untold patient misery,” he said. “Overcrowded departments, overflowing with patients, can result in avoidable deaths.” Hassan and Holland blamed the government’s underfunding of the NHS and social care systems for contributing to hospitals becoming worryingly full.

“The emergency care system is on its knees, despite the huge efforts of staff who are struggling to cope with the intense demands being put upon them. The situation is intolerable for both staff and patients, who are all too often left in the undignified position of waiting on a trolley in a corridor for a bed to become free,” said Hassan, who is an A&E consultant at two hospitals in Leeds.

Separately, the London Ambulance Service is looking into the possibility that problems when its IT system crashed on New Year’s Day contributed to the death of at least one patient. Staff had to make paper records of 999 calls in what one ambulance crew member described as “a shambles”.

The latest official NHS performance figures, released on Friday, showed that A&E units across England were forced to divert patients to nearby hospitals 57 times over the Christmas period. In addition, 34 hospitals said they had experienced major problems coping with demand.