Sitting in the chair beside her hospital bed in a nightie, Elizabeth Lee would much rather be elsewhere – at home. “I’ve been here since mid-September and was told I was fit to leave in late October, but I’m still here”, says Lee, who is 91 – “and a half”, she adds.

“The problem is that they can’t get care in place to let me go home. I feel like I’m stuck here; stuck and isolated. I’m missing being at home. And I’m missing my husband, Fred. We’ve been married for 67 years. If he’s on his own there it means I’m on my own here. The doctor says that as soon as they get care in place I will be going home. But they’ve been telling me that for ages”, adds Lee, for whom ward G4 in Addenbrooke’s hospital, Cambridge, has become her involuntary long-term temporary home.

“I can’t get frustrated as all the staff here have been very kind. But I feel upset about being here. My eyesight’s not good – I’ve got cataracts – so I can’t see very well or read for more than a few minutes. Fred visits me every day, apart from Sunday, when the park and ride isn’t on. But otherwise I just sit in this chair or stay in bed. It’s boring,” she adds.

Lee is the human face of a serious and deepening problem, commonly referred to as “bedblocking”, a major cause of the growing struggle hospitals are facing to cope with an unprecedented number of patients arriving who need treatment, mainly through their A&E departments.

The nonagenarian is typical. She arrived in Addenbrooke’s on 15 September after passing out at home. After several weeks of tests and treatment for a broken rib she was declared fit to go on 28 October, but 72 days on, she is still trapped in hospital. Officially she is a “delayed transfer of care” – a “DTOC” in NHS-speak – waiting, in theory, for the hospital to arrange a package of care support with Cambridgeshire county council to enable her to get back home.

She needs to have carers coming in four times a day to help her with some basic tasks as she cannot walk, the legacy of breaking her back after falling over on snow in the very cold winter of 1963-64. But the reality of her situation is much more complex, and is both gloomy and very sad.

Jenny Abel, the hospital’s lead clinical specialist practitioner for discharge planning, explains that it has proved impossible to arrange help for her, simply because of where she lives – in a village 15 miles from Cambridge. “We just can’t get the care for her,” admits Abel. “The problem is that, although it would be a 15-minute call to see Mrs Lee, it would take 20 minutes to get there from Cambridge and 20 minutes to get back, and that would happen four times a day.

Facebook Twitter Pinterest Occupational therapist Amy Hemus helps Angela Rankin, 68, who suffered a stroke a week ago, in a purpose-built kitchen within Addenbrooke’s hospital. Photograph: David Levene for the Guardian

“But because of that, and because there’s no one else in her village receiving a care package, all of the four care providers who provide those packages – private companies – are saying that they don’t have the capacity to do it. They don’t have enough carers, or they don’t have enough care [to provide to others] in that area to make it viable.”

Hence, someone who is keen and fit to leave the NHS bed she is occupying unnecessarily is unlikely to be able to do so any time soon, because no one can make a profit from her doing so. It is a situation the charity Age UK describes as madness, in which there are only losers and no winners. Crucially, it is causing entire hospitals to get clogged up, leaving them unable to admit new patients as quickly as they deem necessary.

As Chris Hopson, chief executive of NHS Providers, explains: “Delayed discharges are a very significant problem and a major contributor to current performance difficulties in A&E services. If a hospital discharge back door is blocked, wards fill up very quickly and the A&E front door becomes jammed.”

Yet despite the health service’s ability to cope with the growing pressures on it now being seriously questioned by doctors, NHS experts and health union leaders, bedblocking has reached its highest-ever level, with record numbers of patients involved and bed days lost.

Addenbrooke’s, which is among the hospitals worst affected, is a microcosm of wider problems. Currently 87 of its 1,000 beds are occupied by mainly frail, elderly patients classed as DTOCs. That is the largest number it has ever had and is a sharp rise on the 52 seen in September 2013, when it began keeping records. Lee is the DTOC who has been there the longest after her fit-to-go date, although another woman has been trapped for 59 days past hers and another 21 patients for at least three weeks.

The hospital pays a heavy price for all this – patient flow, vital to its smooth running, becomes constricted – though it is an innocent victim of failings elsewhere. “We want to get these patients home. It’s in everybody’s interest for that to happen”, says Tom Bennett, the hospital’s director of operations. “But before they can go they have to be medically safe to go and the care that will be provided to them when they are at home, or at a relative’s or in a care home or nursing home or step-down facility has to be in place.” And that is when things start getting complicated.

Facebook Twitter Pinterest Notice posted outside the entrance to A&E at Addenbrooke’s, which has been forced to cancel operations. Photograph: David Jackson/David Jackson/Demotix/Corbis

“This whole business is hugely frustrating, and it gets upsetting as well. Discharging patients who are usually old and needing ongoing care is complex and sometimes very messy”, says Sandra Myers, the hospital’s director for integrated care. Disputes drag on between the local NHS and the patient’s council over whether a patient’s needs once they are discharged are primarily medical or mainly for social support, and thus who pays. Just when a patient needs the health and social care systems to work together to help them, they find that they are fragmented and sometimes at odds with each other.

As Lee’s case shows, there is too little social care support available – help with washing, dressing or getting out of bed – because Cambridge is too expensive for its poorly paid workforce. A lack of places in care homes in the city is another problem, especially for patients who, while fit to go, need ongoing medical care.

“If a dementia patient needs nursing care, we have on average one bed available in any week in a nursing home for such a patient. That’s part of the reason people get stuck here. If you’re an independent provider [a care home], these types of patients aren’t going to be the most lucrative patients because they are the most needy patients. So care homes can in effect pick and choose which patients they let in. That’s not a criticism; it’s just a fact of life,” adds Myers.

The council is having increasing difficulty finding care homes places available at the “benchmark” maximum prices it is prepared to pay because a mismatch between supply and demand and number of people who fund their own care, has produced a shortage, adds Abel.

Such patients require care homes to have more nurses are on duty and both they and Addenbrooke’s are having trouble recruiting enough for their own purposes. That is one reason why Myers has little luck trying to persuade care homes to upgrade beds for less needy patients to ones for medical cases. The risk of tough inspection is another.

Bedblocking does not just increase the risk of Addenbrooke’s getting jammed up, but having to declare a major incident, as it has done three times in the past three weeks – including on Tuesday night – due to overcrowding, and open as many as six overflow or contingency areas to give it more beds. DTOCs also cost it money from planned operations, such as hip replacements, having to be cancelled. In all 207 such procedures have already been postponed since 1 January because of “lack of capacity” partly due to DTOCs. One week before Christmas, delayed transfers resulted in the loss of 386 bed days.

“These 87 beds are a real loss, both for the patients themselves who are waiting to go elsewhere, and for us, and also for the patients waiting at home to have their hernia repaired or hip replaced, whose operations we have had to cancel,” says Bennett. “It’s a very frustrating problem and one which, with our ageing population, is becoming more problematic over time.”