The NHS faces a mounting beds crisis as care homes suffering unprecedented staff shortages are forced to stop taking patients from hospitals, health and care leaders have warned.

Ministers are desperately trying to free up space in the NHS to tackle a backlog of 5.6 million people – equivalent to almost 10% of people in England – awaiting treatment.

But efforts to speed up the discharge of hospital patients into the community are being hampered by care worker shortages. Britain’s largest not-for-profit care home provider, MHA, has already had to close one in 10 of its homes to admissions from hospitals, its chief executive, Sam Monaghan, told the Guardian.

The warning comes as a comprehensive assessment on Wednesday reveals that care homes in England are facing the biggest staff shortage on record, with 105,000 positions unfilled according to the 2021 State of the Adult Social Care Sector and Workforce report by Skills for Care, an industry body.

Mandatory double vaccination for all frontline workers is now less than a month away, meaning the situation is set to worsen. Monaghan said: “Across the social care sector, the staffing crisis means [fewer] care places for older people. Even as a large charity, MHA was forced to close 10% of our care homes to new admissions on average over the past month, which means more older people are staying in hospital when they don’t need to be there.”

Seven of MHA’s 89 homes remain closed to new residents due to staffing levels, Monaghan added. One area hit particularly hard was Yorkshire, he said, with three MHA homes currently unable to take in people from local hospitals. The crisis underlined the “gap between political aspirations and the reality on the ground for people who need good quality care right now”, he warned.

The workforce shortage is being compounded by a slump in foreign staff coming to fill vacancies, the Skills for Care report shows. Less than 2% of new starters in the first quarter of this year arrived from abroad, compared with more than 8% in 2019 – an estimated drop of about 20,000 people.

Matthew Taylor, the chief executive of the NHS Confederation, said delayed discharges of medically fit patients was having a serious effect on other parts of the health service.

“Health leaders do not want patients who are medically fit and ready to be discharged to have to stay in hospital any longer than they need to as it won’t be the best environment to support their recovery and it means that other patients will have to wait longer for their treatment,” he said. “Increases in delays to discharging patients means fewer inpatient beds available and delays in A&E and elsewhere.”

Last month, Sajid Javid, the health secretary, announced GBP478m in extra funding to enable the quick and safe discharge of patients from hospitals this winter. But experts said the cash would not resolve the shortage of social care workers to look after discharged patients.

“This funding will be welcome but without parallel investment in social care staff to support getting people out of hospital in a timely way and recover closer to home, then patients will face longer waits, or it will be unpaid carers that are left to provide this support,” said Nina Hemmings, researcher at the Nuffield Trust thinktank.

Thousands of staff who are declining Covid vaccinations are expected to be told they can no longer be deployed in care homes in the coming weeks. Many have already quit. Nearly 13% of staff in older adult care homes had not been double vaccinated by 3 October – over 59,000 workers.

Staffing levels in certain areas are likely to be disproportionately hit. Almost one in four care workers in Manchester have not had two jabs, and around one in five in Stoke, Thurrock, and Hackney and Lambeth in London, NHS England data shows.

The government has made double vaccination a “condition of deployment” in care homes in England from 11 November to limit infection spread. Care home operators have called for the deadline to be postponed, pointing out that a similar policy for NHS workers remains under consultation. Nadra Ahmed, the chair of the National Care Association, said it had “succeeded in bringing the sector to its knees”.

A Department of Health and Social Care spokesperson said: “We appreciate the dedication and tireless efforts of care workers throughout the Covid-19 pandemic and beyond. We are providing at least GBP500m to support the care workforce as part of the GBP5.4bn to reform social care. We are also working to ensure we have the right number of staff with the skills to deliver high quality care to meet increasing demands. This includes running regular national recruitment campaigns and providing councils with over GBP1bn of additional funding for social care this year.”