David Cameron is being urged to do more to help tackle the migrant crisis or risk playing into the hands of pro-Brexit campaigners seeking to exploit fears over immigration.

The Prime Minister is under mounting pressure to offer shelter to 3000 unaccompanied migrant children in Europe with Liberal Democrat leader Tim Farron claiming he is "betraying Britain's values".

In a speech today, Yvette Cooper, the former cabinet minister leading a Labour review of the issue, will accuse Mr Cameron of pushing the UK towards leaving the EU by failing to engage with the urgent reforms needed to prevent the situation spiralling.

The pressure comes as Nato defence ministers prepare to consider whether the military alliance could play a role in policing the flow of migrants to Turkey and on into Europe.

Ms Cooper will warn that a fresh surge of new arrivals in the spring will entirely overwhelm Europe unless major steps are taken, such as reimposing national border controls, greater burden sharing and more funds.

"David Cameron has to change tack or he will end up letting the Eurosceptics win," she will claim.

"His strategy on the refugee crisis is to refuse to engage with Europe at all. That won't work. It just makes it harder to get the EU reforms we here in Britain will need, harder to keep stability in Europe."

"We should be in Europe arguing for reform. For all countries to offer sanctuary to refugees and for stronger borders to manage the flow of people and stop criminal gangs.

"For an end to Schengen. For more security checks and rapid asylum assessments. And for every country to do their bit to help rather than the failed relocation scheme that just leaves Germany and Sweden taking all the strain."

Dismissing Eurosceptic arguments, she will say: "Brexit won't magic away the refugee crisis or keep it further from our shores. Quite the opposite.

"Faced with a crisis that crosses borders, unilateralism just won't work.

Mr Farron has invited MPs and campaigners to talks on the practicalities of giving shelter to the young victims of war, accusing ministers of breaching a promise to examine the case.

The PM insists that Britain should concentrate on resettling orphans from the camps in the region rather than those who had made the crossing to Europe.

But the Lib Dem leader said: "During every crisis I can think of, Britain has opened its doors and hearts to those in need.

"We are a beacon of hope and that is something millions of people like myself are proud of. It is what makes me proud to be British.

"This time the Prime Minister has ignored the pleas of charities and frankly he is betraying Britain's values by doing so.

"He clearly isn't willing to lift a finger to help these desperate children, but I refuse to give up. Tomorrow we start the creation of a plan to show the Prime Minister how Britain can take care of 3,000 unaccompanied children."

Mr Farron spoke as it was revealed that deportations to "war-torn" countries of adults who arrived in Britain as unaccompanied children have been "seriously" underestimated by ministers - with more than double the number removed than previously thought.

Newly corrected Home Office figures show that between 2007 and 2015 a total of 3,750 former unaccompanied asylum seeking children were deported to Afghanistan, Albania, Iran, Iraq, Libya and Syria.

It represents a large increase on the 1,616 children initially stated to have been deported in figures released by Immigration Minister James Brokenshire in response to a written parliamentary question from Labour's Louise Haigh.

Ms Haigh said the "astonishing" and "completely unacceptable" mistake which appears to span Tory, coalition, and Labour governments means minsters cannot claim to protect vulnerable people in the immigration system.

Defence Secretary Michael Fallon will be among Nato ministers at a summit in Brussels on Wednesday, where the crisis will be high on the agenda.

Nato secretary general Jens Stoltenberg said the alliance members "see the need to manage and to tackle the human tragedy" and the problems associated with it.

Mr Cameron's spokeswoman said that no request had yet been received for UK resources and personnel for any Nato mission to assist with the Turkish refugee crisis.

She told reporters: "We are supportive of looking at ways to help Turkey deal with the huge burden that it has from refugees.

"We need to look at what would be the most effective way of dealing with that, working with Turkey's neighbours and other partners."

Migration Watch UK suggested the EU could suspend the right of appeal against asylum refusals in a bid to speed the removal of economic migrants from Europe.

It said the move would not be in breach of the Refugee Convention.

Its chairman, Lord Green of Deddington, said: "For so long as every failed asylum seeker has the right of appeal before being sent home, there will in practice be no hope of deterring a continuing, and probably growing, inflow of economic migrants."