David Cameron is set to water down his opposition to allowing unaccompanied child refugees in Europe to enter the UK.

The government will meet with rebel MPs on Wednesday afternoon in an attempt to head off a mass rebellion from Conservative backbenchers. However Cameron may use Prime Minister's Questions today to annouce a compromise.

A deal will need to be struck before Monday, when the House of Commons will vote for a second time on accepting additional child refugees from Europe.

The government has previously opposed the plans, which have been put forward by the Labour peer Lord Dubs, arguing that it will encourage more people to make the perilous journey from the Middle East to Europe and risk their lives with people smugglers.

However, a number of Tories who abstained or voted with the government at the last vote are now expected to vote for Dubs' amendment.

One Christian MP, David Burrowes, who voted with the government on April 25 has said he will "most likely" vote for the amendment to accept child refugees this time. He urged ministers to show "more compassion". Heidi Allen, another lead rebel, abstained from the vote last week. She told BBC Radio 4's Today programme she would "absolutely, 100 per cent" vote for the amendment on Monday.

A new compromise is expected to be announced today. Under the deal Britain would support camps in Europe to process the paperwork more quickly for children with families in the UK. Currently, about three children's paperwork are processed per week.

Save the Children, which has campaigned on this issue alongside Tim Farron, the Christian leader of the Liberal Democrats, says there are "significant numbers" of children in camps in Europe with families Britain.

Steven McIntosh, Save the Children's head of government relations, suggested the move was welcome but hinted it would not be enough. He said: "Any extension of family reunification for lone child refugees in Europe that makes it easier for them to safely join their families is welcome.

"However, we remain concerned about the plight of unaccompanied children who have fled wars and persecution but don't have any family to join – they're on their own and the UK can help to offer them sanctuary."