Britain's government bowed to pressure Wednesday and agreed to take in some unaccompanied children from Syria who have made their way to Europe.

Prime Minister David Cameron's office said children who registered in Greece, Italy or France before March 20 — when the European Union struck a deal to return many migrants to Turkey — would be eligible to come to the U.K. It did not specify how many Britain would accept.

The government said that "the retrospective nature" of its resettlement plan "will avoid creating a perverse incentive for families to entrust their children to people traffickers."

Britain has already agreed to resettle up to 3,000 vulnerable child refugees from the Middle East and Africa by 2020, as well as 20,000 Syrians from Middle Eastern refugee camps.

But the government had argued that accepting children already in Europe would encourage others to make the dangerous journey.

Labour peer Alf Dubs, who came to Britain on the 1930s "kindertransports" of Jewish children from Nazi-occupied Europe, led a campaign to get Cameron's Conservative government to change its mind.

Dubs won the support of some Conservative lawmakers, and the government had faced the risk of defeat in a House of Commons vote on the issue next week.

"I trust the prime minister will be true to his word and move swiftly to ensure the Home Office works closely with local authorities to find foster families to give these young people a stable and secure home," Dubs said.