The government faces a potential Commons defeat over its decision to end the arrival of unaccompanied refugee children under the Dubs scheme, with up to 30 Conservative MPs possibly voting to revive the process.

Ministers announced last month that the numbers arriving under the system, introduced through an amendment by the Labour peer Lord Alf Dubs, who came to Britain as a child refugee before the second world war, was to be stopped at the current 350.

Campaigners had hoped that as many as 3,000 children could be helped. The government said the scheme had to end because no more council spaces were available to accommodate them.

However, some councils have since disputed this, saying they do have the resources to take more unaccompanied minors.

The issue will be the subject of a House of Commons vote on Tuesday when MPs debate amendments attached to the wider children and social work bill, connected to the status of child refugees.

The most significant of these is likely to be one introduced by the Conservative Heidi Allen which is backed by almost two dozen other MPs, among them nine other Tories, including former education secretary Nicky Morgan and former business minister Anna Soubry.

The amendment says each local authority in England should let ministers know their capacity for resettling children. At least once a year, it adds, the government should collate these figures.

Allen said the potential combined support from the Conservative benches totalled 31 MPs based on the number who signed the amendment, as well as MPs who had supported a backbench debate on the issue, joined her in writing a private letter to Theresa May or voted for the Dubs scheme in the first place.

Allen said she was optimistic the government could concede over the issue.

“I’m hopeful that maybe they’ll reach a compromise,” she said. “This is not hard to do. This is not forcing capacity that doesn’t exist. It’s OK for areas like Kent to say ‘no more’; I understand and respect that. But this is a national solution that different parts of the country can respond to differently.

“We know that local authorities out there still have capacity – not all, but a good number. So for me it’s not acceptable that while this remains a real humanitarian crisis, particularly in southern Europe, which does not end at the end of the financial year, so neither should our consultation with local authorities.”

Helping as many unaccompanied child migrants as there was space for was “the moral and the practical thing to do”, Allen said, saying a recent visit to northern France showed children were returning to the Calais area, even after the demolition of its main migrant camp.

“When there are no safe and legal routes they turn to traffickers, as there is no option,” she said. “They are coming back and then it will become our problem, because Kent will be under siege again.”

The rebellion could still be headed off, possibly through government attempts to limit the time for debate, meaning there might be no chance for a vote on the amendments.

There is also the prospect of yet another delaying speech by Philip Davies. The Tory MP, who spoke for 90 minutes last month trying to derail a measure demanding the government ratify a treaty on domestic violence, has tabled an amendment of his own.

This is about another part of the bill – Davies wants to allow parents to opt their children out of sex education classes – but another lengthy address could scupper Allen’s amendment.

Labour’s front bench has also tabled two amendments connected to unaccompanied refugee children, one about the work carried out by councils and another seeking more action by central government.

Angela Rayner, the shadow education secretary, who introduced the amendments along with shadow children’s minister, Emma Lewell-Buck, said Labour wanted to ensure ministers “keep their promises to refugee children”.

She said: “With dozens of their own MPs ready to join the opposition on this, they need to listen before it’s too late.”

The debates come a day after a report by the home affairs select committee called on the government to change its mind on the Dubs scheme.

The committee cast doubt on how thoroughly the government had consulted councils, suggesting that as many as 4,000 extra children could be sheltered if central funding was provided.

It said evidence from charities and other organisations contradicted the Home Office’s assertion that the Dubs scheme would encourage people smugglers.