In a letter to the Prime Minister, the Labour leader urged the Government to work with councils and mayors to ensure rough sleepers can find Covid-secure winter shelter.
Mr Starmer tells the Tory chief: “Rough sleeping is a crisis which you pledged to end for good.
“But it is just the tip of an iceberg – the sharp end of a broken housing system and a society with gaping holes in its safety net.
“Many more people, many of them families with children, will experience homelessness, poverty and destitution this winter.”
Research from the Joseph Rowntree Foundation recently found destitution increased by 54 per cent between 2017 and 2019, with 2.4 million adults and 550,000 children deemed destitute.
Mr Starmer, who is due to leave coronavirus self-isolation on Monday, will hear about homelessness projects in Worcester and virtually meet food poverty campaigners in Birmingham.
In his letter, the Labour leader writes: “Before the Covid crisis, rough sleeping was a shameful sign of Government failure.
“We went into this pandemic with twice as many people sleeping rough than in 2010, affecting towns and cities across the country.
“Thousands of rough sleepers risk missing out on lifesaving shelter this winter unless the Government supports councils and charities to provide Covid-secure shelter.”
A Housing Department spokesman said: “The Government has taken unprecedented action to support the most vulnerable people in our society during the pandemic – backed by over £700 million to tackle homelessness and rough sleeping this year alone, including £23 million in extra support announced today to help rough sleepers recover from drug and alcohol misuse.
“Our work is ongoing and by September we hadsupported over 29,000 vulnerable people, with two-thirds now moved into settled accommodation.
“We’re working with councils, charities and other partners to protect vulnerable rough sleepers this winter and launched the £15million Protect Programme to ensure local areas facing the biggest challenges get the help they need to support rough sleepers.”