Up to 3,000 Syrian and other child refugees from camps in the Middle East and North Africa are to be resettled in Britain over the next four years, the Home Office has announced.

Britain’s new “children at risk” scheme is in addition to the government’s existing programme offering places to 20,000 Syrian refugees by the time of the 2020 general election.

But it will only involve “several hundred” child refugees and their families in the first year and will not offer places to Syrian child refugees currently in European camps, including in Calais.

The announcement by the immigration minister, James Brokenshire, comes in advance of a key Commons vote next week, in the campaign to bring to Britain 3,000 Syrian child refugees in Europe. The House of Lords has already endorsed the demand, and the announcement by Home Office ministers is designed to defuse a potential Conservative backbench rebellion.

It comes as the Home Office confirmed it is to send 75 experts to help implement the controversial EU-Turkey migration agreement in Greece to prevent illegal crossings from Turkey to Greece.

The new Home Office child refugee scheme has been drawn up in association with the United Nations high commissioner for refugees and will be open to all nationalities within the Middle East and north Africa.

It will support vulnerable and refugee “children at risk” and their families, and will not solely target unaccompanied children. Others who may qualify include those threatened with child labour, child marriage and other forms of abuse or exploitation.

Brokenshire said: “We have always been clear that the vast majority of vulnerable children are better off remaining in host countries in the region so they can be reunited with surviving family members. However, there are exceptional circumstances in which it is in a child’s best interests to be resettled in the UK.

“We have engaged with a number of NGOs, including the UNHCR, on the best way to provide protection to refugee children and ensure their welfare and safety remain at the heart of every decision made.

“This new scheme compliments our ongoing work within Europe to assist vulnerable migrant children. This includes the £10m refugee children fund to identify and support vulnerable children and strengthen child protection and family reunification system,” he added.

The UNHCR’s representative to the UK, Gonzalo Vargas Llosa, said the resettlement scheme for refugee children at risk was an important contribution to UNHCR’s continuing efforts to address the global protection needs of refugee children, including through resettlement and other pathways for admission.

“We welcome the scheme’s focus on children at risk, including unaccompanied and separated children, and the UK’s commitment to upholding the principles of child protection and the child’s best interest in implementing the programme,” he said.

The Refugee Council’s chief executive, Maurice Wren, said: “This announcement is life changing, if not life saving news for the small group of children and their families who will benefit.

“However, it’s also grim news for the majority of other refugees who are desperately trying to escape conflict and persecution, who the government is trying to contain in Turkey and other, poorer countries.

“It’s not good enough to offer a lifeline to one group of refugees while colluding to close off the escape routes of everyone else. All refugees need to be able to reach a place of safety. Until we see a coordinated, comprehensive response to this crisis, men, women and children will continue to be forced to take desperate measures to reach safety.”