David Cameron has claimed that the number of people sleeping rough in Britain has fallen under the Coalition – even though official statistics show a dramatic rise on his watch.

On BBC Radio 1's Live Lounge last night the prime minister was asked about help for the homeless by a young woman who had been turned away by her local council when she was living on the street.

Mr Cameron claimed rough sleeping had gone down under his watch despite huge cuts to council budgets that local politicians say have put local services under pressure.

"We're got to house the homeless and local authorities do have a duty to house people who have nowhere to go. That is happening in most cases, it needs to happen in every case," he said.

"... We've got to help people who are sleeping rough, and their numbers are down under this government, we've been getting them into shelters."

But the prime minister's claim appears to be contradicted by official statistics released by the Department for Communities and Local Government.

According to DCLG stats homelessness rose from 1,768 in 2010 to 2,744 by 2014, the last year with full statistics on record.

The rise means rough sleeping in England has risen by more than half - 55%.

Matt Downie, a policy director at the homelessness charity Crisis, said after the broadcast that the prime minister had "got his facts wrong".

“Last night on BBC Radio 1's Live Lounge, Prime Minister David Cameron was questioned on the lack of help for single homeless people. Sadly, the Prime Minister got his facts wrong," he said.

"On three occasions he claimed that rough sleeping has gone down over the past five years. However, the Government’s own statistics show that in fact rough sleeping in England has risen by 55% since 2010, and by 14% in the past year (see notes for graph).

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“Tragically, rather than get the help they need, many homeless people who ask their councils for help are being turned away to sleep on the streets – cold, desperate and forgotten.

"That’s why we’re calling on all political parties to commit to reviewing the help single homeless people get under the law. In this day and age, no-one should be forced to sleep rough.”

Homelessness is primarily dealt with by local authorities, which is a matter for the devolved administrations in Scotland, Wales, and Northern Ireland.