Home Secretary Theresa May agreed to admit a few hundred Syrian refugees yesterday amid allegations that Britain is snubbing a bigger UN-backed scheme.

Ms May told MPs that Britain's scheme would focus on giving refuge to survivors of torture and violence, women and children in need of medical care and victims of sexual violence.

She said "several hundred" refugees would be admitted under the new programme, in addition to nearly 3,500 Syrian asylum-seekers who were already in Britain.

"This programme will run in parallel with the UN High Commissioner for Refugees own programme," said Ms May.

She said that 11 million Syrians were in desperate need, with 6.5m people displaced inside the country, and 2.3m refugees in neighbouring countries. Britain had already provided £600 million of relief aid, she added.

When Labour MPs demanded why Britain was not joining the UNHCR refugee scheme, she replied that the government wanted "a degree of flexibility."

Cynon Valley MP Ann Clwyd suggested that the government had not joined the UNHCR programme because Britain's efforts compared poorly with Germany's offer to admit 10,000 Syrian refugees.

Labour shadow home secretary Yvette Cooper welcomed the government's reversal of its refusal last week to announce a scheme for Syrian refugees.

She suggested the change was a result of Labour pressure in Parliament. Left MP Jeremy Corbyn and veteran MP Gerald Kaufman raised urgently the plight of 560,000 Palestinian refugees "marooned" in Syria and facing starvation.

Mr Kaufman told MPs: "In the Yarmouk camp they are dying of starvation and their food consists of grass and animal food."

Mr Corbyn said: "Many of the Palestinian refugees in Syria are themselves refugees from Iraq and indeed often before that many other countries in the region.

"I would hope that you will be able to look very carefully and very sympathetically at the plight of people that have been driven from pillar to post by the travails and history of the whole region and give them at least a place of safety here?"

Ms May claimed that Britain was helping Palestinian refugees who had left Syria, but there was "lack of access" to those inside the country.