The British Government has been urged to harness the "huge support" for refugees fleeing conflict as MPs warned the country will struggle to cope with 20,000 people re-settling in the next five years.
The Home Affairs Select Committee of MPs has today warned of the "huge change in the scale" in the number of refugees the UK is accommodating.
Chairman Keith Vaz points out the 4,000 refugees per year is in stark contrast to 1,039, the highest annual number resettled in the last ten years.
Ministers have so far refused to say how many people have already arrived in the UK - though Mr Cameron said he hoped 1,000 would arrive by the end of the year - leading to fears about its action plan.
The MPs call on ministers to think again about rejecting the offer from thousands of members of the public to put refugees up in their homes.
"At no point in the recent past has the UK come near to resettling 4,000 refugees in one year," the committee's report says.
Labour MP, Yvette Cooper, who chairs Labour's refugee taskforce, told The Huffington Post UK the Government can do better, arguing Britain accepted 4,000 Bosnian refugees in 1992 within weeks of them being displaced by the conflict in the Balkans.
Yvette Cooper in Lesbos: "The refugee crisis is getting worse not better."
Ms Cooper, former Shadow Home Secretary who has just returned from the Greek island of Lesbos where thousands of refugees Syrian and Iraqi refugees are holed up, has called on David Cameron to lead a Europ-wide humanitarian effort.
She told HuffPostUK: "The refugee crisis is getting worse not better.
"That's why all countries have to act. As the Home Affairs Select Committee report says, there needs to be proper support for local authorities to do so.
"In 1992 Britain took in 4,000 Bosnian refugees in just a few weeks and each year we receive 25,000 asylum applications from all over the world.
"There's strong support from community groups, faith groups and local councils right across the country for Britain to go further and faster to help refugees than the 4,000 a year the Government has currently pledged.
"The Government need to work with councils and communities to make this happen because we cannot turn our backs."
The number of refugees the UK has taken since 2004 under three schemes
Pop star Bob Geldof is among the high-profile names to have volunteered accommodation to deal with Europe's biggest refugee crisis since the Second World War. Around 4,500 people have said they are willing to find a bed.
Mr Vaz said the refugee crisis had reached an "unimaginable scale" this summer.
"The generosity of the British public in offers of assistance and even space in their homes has not been accepted by ministers. This should be reconsidered," he said.
"Housing is likely to be one of the most difficult issues and it may be that, properly organised and supported, offers of private accommodation will be a helpful, viable and perhaps essential part of the solution."
The UK has agreed to accept 20,000 refugees by 20,000
Richard Harrington, minister responsible for Syrian refugees, said the government planned to resettle 1,000 Syrians "by Christmas".
"We have already welcomed and successfully resettled a number of vulnerable people who were in desperate need of our help," he said.
"The scale of the expansion needs careful planning to ensure we get it right."