The Government has backtracked on its refusal to resettle refugee children who have already reached Europe by letting local councils take in more unaccompanied minors from Greece, Italy and France.

Angus Robertson, the Scottish National Party’s leader in Westminster, challenged David Cameron on the issue at Prime Minister’s questions.

While insisting he would “stick to the principle” of resettling children from refugee camps in the Middle East and North Africa because the Government did not want to encourage more treacherous sea journeys, the Prime Minister hinted at other changes.

“We’re already taking child migrants in Europe with a direct family connection to the UK and we will speed that up,” Mr Cameron said.

Syrian refugee children stand at a fence in Nizip district near Gaziantep, Turkey (EPA)

“We are also talking to Save the Children to see what more we can do, particularly with children who came here (to Europe) before the EU-Turkey deal was signed.

“What I don't want us to do is to take steps that will encourage people to make this dangerous journey because otherwise our actions, however well-meaning they will be, could result in more people dying rather than more people getting a good life.”

He said the UK would not opt in to "failed" European Union resettlement quotas and argued that comparing the issue to the Kindertransport that saved children from the Nazis was an "insult" to the countries involved.

But Mr Cameron confirmed that there is no longer a set number of refugee children in an amendment to the Immigration Bill, allowing the Government to "go round" British councils to see what more they can do.

A spokesperson for Downing Street said children registered as asylum seekers in Greece, Italy or France before 20 March would be eligible for resettlement.

Those deemed to be vulnerable to trafficking or exploitation will be prioritised as part of work with the UN Refugee Agency and Save the Children.

Children play among cubicles that contain bunk beds in Berlin (Getty)

"The Government is not putting a fixed number on arrivals, but will instead work with local authorities across the UK to determine how many children will be resettled," Downing Street said.

"We will move quickly to consult local authorities, with the first arrivals expected before the end of the year."

The initiative will be on top of a previous proposal for unaccompanied children and the UK's pledge to take 20,000 Syrian refugees over five years.

Campaigners said the Government's existing plans to take in up to 3,000 children from refugee camps in the Middle East and North Africa were “not good enough” last month.

That proposal was announced days before a crucial vote in the House of Commons on a rival plan to take in unaccompanied minors who have already risked their lives to reach Europe.

Humanitarian organisations say thousands of children are trapped across the continent, sleeping rough or in squalid camps and detention centres where they are left vulnerable to exploitation and abuse.

Mr Cameron has previously insisted the children who have succeeded in reaching Europe are not in immediate danger as they are no longer in a conflict zone and they should be looked after as near to their home countries as possible.

David Cameron attacked over refugee vote

Some ministers have also argued that taking in unaccompanied minors from camps such as the Jungle in Calais would simply encourage more to make treacherous journeys across the Mediterranean and Aegean seas.

Tory backbencher Heidi Allen - who abstained when the issue was last debated by MPs - said that ministers faced defeat at the hands of Conservative rebels unless they gave ground.

"It is not relatively safe to be pulled into trafficking and prostitution. Talk to the doctors there - Medecins Sans Frontieres - they are literally stitching up children on a daily basis and sending them back to the camps,“ she told the BBC Radio 4 Today programme.

"That is not the safety that you and I think of when we think of Europe. These children are not safe at all. They need our help."

Pressure on ministers intensified with the intervention of a former Jewish child refugees from the Nazis, urging them to offer sanctuary to those in need.

In a letter to the Prime Minister, Sir Erich Reich, chairman of Kindertransport-Association of Jewish Refugees, appealed to him to "demonstrate compassion", while an amendment to the Immigration Bill to take refugee children from within Europe was started by another refugee from the Nazis, Lord Dubs.

Refugee crisis - in pictures Show all 27 1 /27 Refugee crisis - in pictures Refugee crisis - in pictures A child looks through the fence at the Moria detention camp for migrants and refugees at the island of Lesbos on May 24, 2016. AFP/Getty Images Refugee crisis - in pictures Ahmad Zarour, 32, from Syria, reacts after his rescue by MOAS (Migrant Offshore Aid Station) while attempting to reach the Greek island of Agathonisi, Dodecanese, southeastern Agean Sea Refugee crisis - in pictures Syrian migrants holding life vests gather onto a pebble beach in the Yesil liman district of Canakkale, northwestern Turkey, after being stopped by Turkish police in their attempt to reach the Greek island of Lesbos on 29 January 2016. Getty Images Refugee crisis - in pictures Refugees flash the 'V for victory' sign during a demonstration as they block the Greek-Macedonian border Refugee crisis - in pictures Migrants have been braving sub zero temperatures as they cross the border from Macedonia into Serbia. Refugee crisis - in pictures A sinking boat is seen behind a Turkish gendarme off the coast of Canakkale's Bademli district on January 30, 2016. At least 33 migrants drowned on January 30 when their boat sank in the Aegean Sea while trying to cross from Turkey to Greece. Getty Images Refugee crisis - in pictures A general view of a shelter for migrants inside a hangar of the former Tempelhof airport in Berlin, Germany Refugee crisis - in pictures Refugees protest behind a fence against restrictions limiting passage at the Greek-Macedonian border, near Gevgelija. Since last week, Macedonia has restricted passage to northern Europe to only Syrians, Iraqis and Afghans who are considered war refugees. All other nationalities are deemed economic migrants and told to turn back. Macedonia has finished building a fence on its frontier with Greece becoming the latest country in Europe to build a border barrier aimed at checking the flow of refugees Refugee crisis - in pictures A father and his child wait after being caught by Turkish gendarme on 27 January 2016 at Canakkale's Kucukkuyu district Refugee crisis - in pictures Migrants make hand signals as they arrive into the southern Spanish port of Malaga on 27 January, 2016 after an inflatable boat carrying 55 Africans, seven of them women and six chidren, was rescued by the Spanish coast guard off the Spanish coast. Refugee crisis - in pictures A refugee holds two children as dozens arrive on an overcrowded boat on the Greek island of Lesbos Refugee crisis - in pictures A child, covered by emergency blankets, reacts as she arrives, with other refugees and migrants, on the Greek island of Lesbos, At least five migrants including three children, died after four boats sank between Turkey and Greece, as rescue workers searched the sea for dozens more, the Greek coastguard said Refugee crisis - in pictures Migrants wait under outside the Moria registration camp on the Lesbos. Over 400,000 people have landed on Greek islands from neighbouring Turkey since the beginning of the year Refugee crisis - in pictures The bodies of Christian refugees are buried separately from Muslim refugees at the Agios Panteleimonas cemetery in Mytilene, Lesbos Refugee crisis - in pictures Macedonian police officers control a crowd of refugees as they prepare to enter a camp after crossing the Greek border into Macedonia near Gevgelija Getty Images Refugee crisis - in pictures A refugee tries to force the entry to a camp as Macedonian police officers control a crowd after crossing the Greek border into Macedonia near Gevgelija Getty Images Refugee crisis - in pictures Refugees are seen aboard a Turkish fishing boat as they arrive on the Greek island of Lesbos after crossing a part of the Aegean Sea from the Turkish coast to Lesbos Reuters Refugee crisis - in pictures An elderly woman sings a lullaby to baby on a beach after arriving with other refugees on the Greek island of Lesbos after crossing the Aegean sea from Turkey Getty Images Refugee crisis - in pictures A man collapses as refugees make land from an overloaded rubber dinghy after crossing the Aegean see from Turkey, at the island of Lesbos EPA Refugee crisis - in pictures A girl reacts as refugees arrive by boat on the Greek island of Lesbos after crossing the Aegean sea from Turkey Getty Images Refugee crisis - in pictures Refugees make a show of hands as they queue after crossing the Greek border into Macedonia near Gevgelija Getty Images Refugee crisis - in pictures People help a wheelchair user board a train with others, heading towards Serbia, at the transit camp for refugees near the southern Macedonian town of Gevgelija AP Refugee crisis - in pictures Refugees board a train, after crossing the Greek-Macedonian border, near Gevgelija. Macedonia is a key transit country in the Balkans migration route into the EU, with thousands of asylum seekers - many of them from Syria, Afghanistan, Iraq and Somalia - entering the country every day Getty Images Refugee crisis - in pictures An aerial picture shows the "New Jungle" refugee camp where some 3,500 people live while they attempt to enter Britain, near the port of Calais, northern France Getty Images Refugee crisis - in pictures A Syrian girl reacts as she helped by a volunteer upon her arrival from Turkey on the Greek island of Lesbos, after having crossed the Aegean Sea EPA Refugee crisis - in pictures Refugees arrive by boat on the Greek island of Lesbos after crossing the Aegean sea from Turkey Getty Images Refugee crisis - in pictures Beds ready for use for migrants and refugees are prepared at a processing center on January 27, 2016 in Passau, Germany. The flow of migrants arriving in Passau has dropped to between 500 and 1,000 per day, down significantly from last November, when in the same region up to 6,000 migrants were arriving daily.

The proposal was due to be voted on again next week but Mr Cameron said the step was no longer needed and the Bill would not be sent back to the House of Lords.

Downing Street said on Wednesday that it had "responded" to the campaign and would accept the revised amendment put forward by Lord Dubs, when it returns to the House of Commons next week.

Lord Dubs said he welcomed the Government's decision and hoped it would help "ease the plight of some of the unaccompanied child refugees in Europe".

He added: “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.”

The Refugee Council said the announcement only raised the policy of "limited chances" for lone children to find safety in Britain.

Dr Lisa Doyle, the charity's head of advocacy, said: “However, we shouldn’t be fooled into thinking the Government has suddenly discovered its conscience while it’s simultaneously vilifying asylum seekers who are already in the UK and doing its best to trap all other refugees in poor countries.

“The British public have made themselves clear – refugees’ lives matter. The Government must stop trying to outsource its wider responsibilities and instead act quickly and generously to offer refugees safe passage.”