The number of homeless cases involving someone suffering from a mental or physical illness has skyrocketed since 2010

Homelessness among people with mental and physical health problems has increased by around 75% since the Conservatives came to power in 2010, and there has been a similar rise in the number of families with dependent children who are classed as homeless.

According to official figures collated by the Department for Communities and Local Government, the number of homeless households in England identified by councils as priority cases because they contain someone who is classed as vulnerable because of their mental illness, has risen from 3,200 in 2010 to 5,470 this year.

Over the same period, the number of families with dependent children – another priority homeless group identified by councils – has increased from 22,950 to 40,130. The number of homeless households with a family member who has a physical disability has increased from 2,480 to 4,370.

After a week in which the prime minister has come under renewed attack over homelessness, housing charities have called on the government to urgently build more affordable housing and reverse a squeeze on benefits which has left vulnerable people unable to pay their rents.

“With homelessness soaring, it is no surprise that the number of vulnerable groups – including families with children – who are having to turn to their council for help is on the rise,” said Polly Neate, chief executive of charity Shelter. “As wages stagnate, rents continue to rise and welfare is cut, many people are struggling to keep a roof over their head. Eviction is now the number one cause of homelessness.

“Our services across the country are seeing an increase in the number of people with multiple and complex needs, and we think this may be because other services are failing to provide the help that people need. The solution to our housing crisis must be to urgently build more affordable homes and, in the short term, end the freeze on housing benefit that is increasingly pushing people over the precipice into homelessness.”

Last week, Theresa May was accused of failing to understand the plight of homeless families following her House of Commons response to Rosena Allin-Khan, the Labour MP for Tooting, who said 2,500 children in her constituency would “wake up homeless on Christmas Day”.

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May said: “Anybody hearing that [question] will assume that what that means is that 2,500 children will be sleeping on our streets. It does not.”

She added: “It is important that we are clear about this for all those who hear these questions because, as we all know, families with children who are accepted as homeless will be provided with accommodation.”

Her comments attracted criticism from homeless charities and opposition MPs. “The scale of rising homelessness shames us all,” said John Healey, Labour’s shadow housing secretary. “After seven years of failure on housing, falling homelessness under Labour has turned into rising homelessness under the Conservatives.

“There was an unprecedented decline in homelessness with the last Labour government, but the number of homeless households has increased by half since 2010 and it is some of the most vulnerable groups who have been worst affected. It doesn’t have to be this way. Ministers need to get a grip.”

Labour has set out its plans to tackle homelessness with a new national mission to end rough sleeping within the next parliament.

In his Christmas address), Jeremy Corbyn identified homelessness as a key issue as he called for people to show care and love to others. “It’s a time of the year when we think about others, like those who have no home to call their own or who are sleeping rough on our streets,” the Labour leader said.

“Tackling homelessness is a complex issue with no single solution but we’re determined to help the most vulnerable in our society,” a government spokesman said. “While the number of those accepted as statutory homeless peaked at over 135,000 in 2003-04 and is now well below this level, we know much more needs to be done.

“That’s why we’re providing over £1bn through to 2020 to reduce all forms of homelessness and rough sleeping, bringing in the most ambitious reform in decades through the Homelessness Reduction Act to ensure people get support sooner, and trialling Housing First to help the most entrenched rough sleepers.”