David Cameron faces the possibility of a humiliating Commons defeat on Monday over policy on child refugees, as Tory MPs demand that the UK admits more unaccompanied young people who have fled to Europe from their war-torn homelands.

At least a dozen Tory MPs were said to be considering whether to back an amendment to the immigration bill, tabled by Labour peer Lord Dubs and backed by the House of Lords last month, which commits the UK to take in 3,000 lone child refugees who are already in Europe.

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Dubs, who was saved from the Nazis and brought to London in 1939 as part of the Kindertransport programme, has led a parliamentary campaign to take in youngsters from camps near Calais and elsewhere in Europe who, he says, are hugely vulnerable to exploitation, sexual violence and disease.

With the government’s Commons majority just 18, a rebellion by a dozen Tories could be enough to inflict defeat if the other parties marshal their forces to vote for the Dubs plan.

In an attempt to buy off rebels, ministers reiterated last week a pledge to admit 3,000 more migrants by 2020, most of them children, but have insisted that these will come from camps in the Middle East and north Africa – an approach that is seen as inadequate by Labour, the Liberal Democrats and charities led by Save the Children.

Heidi Allen, Tory MP for South Cambridgeshire, has made it clear that the government should admit young people who have reached Europe, not just those in camps. On her website, she says the government needs to “do more” and insists she will “work tirelessly with my colleagues to ensure the UK plays its part in addressing the humanitarian crisis we are facing”.

Tory MP Dan Poulter, a former health minister, said he was considering the merits of the Dubs amendment. “There is a crisis right here in Europe, right now, that needs addressing. While it is right that we should help those in camps in the Middle East and north Africa, we also need to help those who have already arrived on our doorstep in Europe. This would be consistent with Britain’s historic approach of providing refuge and asylum to those in greatest need.”

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The key Commons vote comes as new research from Citizens UK has identified 157 children who are living alone in the Calais Jungle camp who have close family members in Britain and should be reunited here.

The Liberal Democrats’ leader, Tim Farron, said: “The government has tried to muddy the water with a concession that will not help a single child who is alone and vulnerable in Europe. The orphan children I have met need help and hope. Our government can offer that.”

Yvette Cooper, chair of Labour’s Refugee Taskforce, said: “95,000 child refugees are alone in Europe. In Greece and Italy, children’s homes are full and thousands of children and young people are sleeping rough, at serious risk of exploitation and abuse. MPs on all sides believe Britain can and should be doing more to help these children. It’s time we did so by voting for Alf Dubs’s amendment on Monday.”

Parliament’s international development committee recommended the resettlement of 3,000 children from within Europe, after warnings from humanitarian organisations that thousands of unaccompanied children were vulnerable to exploitation and violence and were living in appalling conditions.