The prime minister is to set out details of government plans to resettle more refugees from Syria when MPs return from the summer recess later.
David Cameron is expected say how many people the UK will accept, having said previously it would be “thousands”.
He has said the refugees will come from camps bordering Syria rather than from among those already in Europe.
On Sunday Chancellor George Osborne said the international aid budget would be used to help councils house people, reports the BBC.
European countries are dealing with a surge of people fleeing the Middle East and other regions, particularly from Syria, Afghanistan and Eritrea.
Thousands have made their way through Austria since Hungary removed restrictions on transit on Friday. From there, they have been travelling to Vienna and on to Germany.
About 18,000 asylum seekers arrived in Germany over the weekend, officials there said.
The country’s coalition government has said it will release billions of euros to help federal states and municipalities cope with the record numbers of migrants.
Last week Cameron said accepting more people was not the simple answer to the situation but calls for the UK to take in more refugees intensified after the publication of a picture of the body of a drowned three-year-old Syrian boy, Alan Kurdi, washed up a Turkish beach.
A petition calling for Britain to take more refugees has received more than 420,000 signatures – although a petition saying no more immigrants should be allowed into the UK has received more than 71,000 signatures.
During a visit to Portugal and Spain on Friday Cameron said Britain would take refugees directly from the camps in countries bordering Syria – avoiding the need for them to put themselves in the hands of people traffickers.
Cameron’s plan to take in thousands more refugees suggests he may expand the Syrian Vulnerable Persons Relocation (VPR) scheme – although this has not been confirmed.
Under VPR, 216 Syrians have been brought to the UK since March 2014.
People brought to Britain under VPR have been granted Humanitarian Protection, a status normally used for people who “don’t qualify for asylum” but would be at “real risk of suffering serious harm” in their home country.
They can stay for five years, have the right to work and access public funds. After five years they can apply to settle in the UK.
Osborne sought to reassure Conservative MPs concerned about the costs of taking in refugees, telling the BBC’s Andrew Marr Show on Sunday that funds would be channelled from the international aid budget to local councils to pay for housing and other services.
He also said ministers should make the argument for taking military action against Islamic State militants in Syria.
