Council chiefs have warned David Cameron that he must make resources available to support essential public services if Britain is to open its doors to a new wave of Syrian refugees.
In the face of intense political pressure, the Prime Minister announced on Friday that the UK would resettle "thousands more" people from the refugee camps in the countries bordering Syria.
Labour leadership contender Yvette Cooper said already 40 councils across Britain had responded to her appeal to offer sanctuary to people fleeing the country's bloody civil war.
However the Local Government Association (LGA) warned significant sums were already being spent supporting refugees in the UK and that additional funding from Whitehall would be needed.
David Simmonds of the LGA's asylum, refugee and migrant task force said councils in England were currently taking 2,000 unaccompanied refugee children a year at a cost of £50,000 for each child.
A further £150 million-a-year was being spent on destitute families who had had their asylum applications turned down but who remained in the UK.
"If we are going to scale those numbers up significantly we need to make sure that those kinds of resources are available to England's councils and also other public services to make sure that we have what is required in terms of school places, hospital beds, GPs that sort of thing," he told the BBC Radio 4 Today programme.
He said councils would welcome it if other families followed the example of Bob Geldof, who has offered to put up four refugee families at his homes in Kent and London.
However he suggested the priority would be to place refugees who were already in the UK rather than those awaiting re-settlement from the camps.
"I am sure that many local councils would be delighted if those who have got space are making that offer because I am sure that we could offer those places to some of the refugee families who are already in the UK," he said.
Ms Cooper - who earlier this week called for the UK to take 10,000 refugees - said local authorities around the country had shown a "rising sense of moral purpose" and it was now up to the Government to respond.
The shadow home secretary said that within 24 hours of her asking councils in England, Scotland and Wales asking if they would be prepared to help in providing places for refugees, more than 40 had written back offering support.
"There is a real determination and rising sense of moral purpose across Britain to help desperate families. But now the Prime Minister needs to match it," she said.
Mr Cameron said the UK would act with "our head and our heart" with a major expansion of an existing programme to resettle vulnerable refugees from the camps bordering Syria.
Critics complained his statement said nothing about helping the tens of thousands who have flooded into the EU and are struggling to make their way across the continent in the hope of claiming asylum in the wealthier nations of the north.
However a Populus poll of 1689 people, reported in The Times, suggested the country was divided over the right response to the crisis with a narrow majority - 51% - saying that they did not believe the Government needed to go any further.
So far, just 216 Syrians have been admitted to the UK under the scheme to help the most vulnerable people in refugee camps, while a further 5,000 have been granted asylum over the past four years.