Care home leaders are urging the government to lift restrictions on low-paid foreign workers entering the UK to help solve a staffing crisis, which could be exacerbated by more than 70,000 staff being forced out in November if they do not get fully vaccinated.

Care England, which represents the largest private care home chains, said ministers should cut the qualifying salary level for overseas recruitment of social care staff from £25,600 and add all care workers to the shortage occupation list used to grant visas. Currently the list includes only care managers and senior care staff rather than rank and file, even though some operators are facing such extensive shortages that they are having to turn down care requests.

“Quite simply care providers are at breaking point,” said Prof Martin Green, the chief executive of Care England. “The writing is on the wall and without immediate help, as given to the NHS, the social care sector will crumple and not be there to support the NHS over the winter let alone in years to come.”

More than one in six care staff in England have yet to receive two doses of Covid vaccine leaving 76,000 eligible staff at risk of being forced to quit after 9 November when vaccination against the virus will become a condition of employment. Before the pandemic there were already about 112,000 care vacancies in England with jobs paying £8.50 an hour on average, according to Skills for Care, an industry organisation. Staff shortages in other sectors such as hospitality and warehouse distribution mean exiting care workers have little difficulty finding often better paid alternative work.

The government has already asked the migration advisory committee to assess the impact on adult social care of ending freedom of movement after Brexit, but it is not due to report back until April 2022.

Care England has also asked the health and social care secretary, Sajid Javid, to waive the immigration skills charge for care workers and fast-track visas under sponsorship licences.

Care operators have reported a fall in the number of foreign workers seeking jobs and an increase in the numbers leaving to return home. The majority of the adult social care workforce is British, but about 113,000 jobs were occupied by EU nationals and 134,000 jobs by people from other countries.

The UK’s second-largest private care home operator, Barchester, has separately warned that last week’s announcement of a tax rise to pay for NHS and social care changes will place further strain on recruitment. Pete Calveley, its chief executive, said the tax rise will cost his 17,000 staff about £6m a year and his company around the same amount.

“At a time when it is very difficult to recruit staff into social care we have less money to increase their salaries,” he told the Guardian. “It is just utter madness and I can’t believe this is what they have done.”

A government spokesperson indicated it would not meet Care England’s request. “We want to see employers make long term investments in the UK domestic workforce instead of relying on labour from abroad,” they said.

“The vast majority of care staff are already vaccinated and we are focusing on encouraging even more staff to get jabbed to protect their colleagues and those they care for.”