More than a million people over 65 live in areas in England where there are no care home beds, a charity has said.

A study commissioned by Age UK found that large swathes of the country were “care deserts” lacking residential care or nursing homes.

Caroline Abrahams, the charity’s director, said the research showed how “chaotic and broken” the market for care had become after years of underfunding. “If the awful situation set out in this report does not persuade our government to finally get a grip and take action, I don’t know what will,” Abrahams said.

The study, conducted by Incisive Health, an independent health consultancy firm, found that more than one in four postcode areas in England – 2,200 out of around 7,500 – had no residential care provision. Two-thirds (5,300) had no nursing homes, for people with more acute problems.

The report said more than 1.3 million over-65s lived in these areas and risked being unable to get support if they needed it.

The study found that a big driver of the problem was a lack of staff. Vacancy rates for nurses in social care rose to 12.3% in 2017/18. The report said staffing was a particular problem in the south-east, and that high numbers of EU staff in the sector, many of whom have left or are planning to leave, could mean extra disruption from Brexit.

Abrahams said: “The report shows what an impossible position local authorities are in. They are supposed to manage their local care market, but they lack the levers to do so, and the big drivers of the problems in the care industry are way beyond their control.

“Meanwhile, they are desperately short of money to purchase care home places for older people in need, so more and more of the financial burden is being shifted on to those older people who fund their own care, who are paying through the nose to keep the system afloat. This is deeply unfair.”

Age UK estimates that public spending on social care has declined by £160m in the last five years despite rising demand.

The government has repeatedly delayed publishing a green paper on a new long-term funding model. The paper will build on an additional £2bn the government has provided to meet social care needs and reduce pressures on the NHS.

The Department for Health and Social Care has been approached for comment.