The UK government is being urged to move rapidly to help stranded families of British foreign fighters in Syria, including giving them access to cash, aid and indirect advice on how to return from British-funded aid agencies working in Syria.

Thousands more Islamic State fighters and their families surrendered to the US-backed Syrian Democratic Forces (SDF) on Tuesday, placing a fresh burden on the overcrowded al-Hawl refugee camp in which the son of 19-year-old Shamima Begum died last week. The camp is close to the Iraq border and is controlled by the SDF.

Begum was stripped of British citizenship by the Home Office, but the foreign secretary, Jeremy Hunt, said on Sunday he was working jointly with the Department for International Development (DfID) to rescue vulnerable children of British fighters. Since then no proposal has emerged and Whitehall officials have stressed they are not planning to send Foreign Office officials to the area.

Lloyd Russell-Moyle, a Labour member of the international development select committee, said it would be safe to to rescue the children. “The refugee camp is managed by the UK’s principal allies against Islamic State on territory on which we have troops stationed and hundreds of journalists visit each year,” he said. “The government should stop thinking aloud and start taking this seriously.”

Russell-Moyle, who has visited Kurdish Syria, added that leaving British children to die in refugee camps was “unconscionable”.

Facebook Twitter Pinterest The al-Hawl refugee camp. Photograph: Achilleas Zavallis/The Guardian

The Foreign Office is not operating in Syria but does fund UK aid agencies in the al-Hawl camp in the north-east of the country, to which partners of foreign fighters have fled or been transferred. In the absence of a British government presence, the agencies may be able to transfer the British women and children to the nearby Syrian-Iraq border, where they could receive British consular advice, including about the terms on which they would be allowed to return home.

There is a broad consensus across Whitehall that the status quo is not sustainable since the number of wives of British foreign fighters in the camp is far higher than forecast. A total of 12,000 women and children of all nationalities have arrived from Isis-controlled Baghuz in eastern Syria since Wednesday morning, bringing the total population at al-Hawl to more than 65,000, the International Rescue Committee has reported.

The UN High Commission for Refugees said there were 3,000 children from 43 countries living in the camp, along with many more Syrian and Iraqi children, in “extremely dire conditions”. It is possible as many as one in four are under the age of five.

Among the children are British citizens. They have UK citizenship as long as they were born before their mothers’ citizenship was revoked.

Alistair Burt, who doubles as a minister at the Foreign Office and at the DfID, told MPs it was right to provide help. “DfID-funded partners are providing support, including medical screening on arrival at the camp; medical services for children through mobile medical teams; clothing for children; mental trauma counselling for children; child protection checkpoints for unaccompanied or separated children; and activity tents for children.”

But he also hinted at relaxing the ban on British cash transfers to the partners of foreign fighters, saying: “There is little evidence of any abuse, and it can be a most practical way of delivering aid.”

The international development secretary, Penny Mordaunt, has banned such cash transfers in order to ensure that there “was no risk of divergence to terrorist sources”. But with the collapse of Isis in Syria and Iraq, that risk is reduced.

The plight of the children of foreign fighters is causing concern across Europe. A French test case is seeking to prove that France’s refusal to offer a right of return to children would be in breach of the provisions of the UN convention on the rights of the child, to which Paris is a signatory, as well as the European convention on human rights.

UK law allows Britain to revoke the citizenship of anyone who commits a serious crime, so long as they retain citizenship status elsewhere as rendering a person stateless is illegal under international law.

The UK is also considering the provision of funds to help the Syrian Kurdish government try male foreign fighters either in their jurisdiction or in neighbouring Iraq, a route adopted by France. Only 10% of foreign fighters returning to the UK have been prosecuted successfully so far, partly due to a lack of evidence that can be used in a British court of law.