The former Shadow Foreign Secretary repeated her call for Britain to take 10,000 refugees immediately alongside help for unaccompanied children as it emerged 50,000 people had descended on a Turkish border crossing.
Migration both from within and outside the European Union is set to be a major issue in the forthcoming referendum over Britain’s membership and the Normanton, Pontefract and Castleford MP argued it underlined the need for a ‘remain’ vote.
Ms Cooper said: “What it shows is that actually, when you are dealing with something that’s such a big global problem you need countries to work together. I think we would find it much harder to deal with the refugee crisis if we were out of Europe.
“We would find it harder to maintain our border checks in Calais rather than Dover that would cause big challenges for managing what happens.
“We would also find it harder to get other countries whether it be Greece, whether it be Germany, whether it be other countries across Europe, to also be working together both to put pressure on the Syrian process but also to be able to have border checks, to have robust checks in place and to give sanctuary.”
David Cameron has committed Britain to accepting 20,000 refugees over the next five years taken from camps around the Syrian border.
But Ms Cooper, who last year visited the Greek island of Lesbos to see the scale of the crisis, urged the Government to speed up the process and welcome more refugees in the shorter term.
“I originally said Britain should take 10,000 straight away. If every city, every county across the country simply supported 10 refugee families that in itself makes 10,000 people. You could do that in a year,” she told Sky News.
Agreeing there were concerns about the impact of accepting so many refugees, she said: “People have become more worried and I think part of the reason people have become more concerned is because they don’t see the plan, where is the comprehensive plan across Europe.”
Ms Cooper added: “My argument has always been this has got to be done with a plan that involves both sanctuary and border controls and checks.”
Ms Cooper’s backing for Britain to stay in the EU coincided with criticism from Conservative Party activists over Mr Cameron’s suggestion that MPs should not listen to their local parties when deciding which side to back in the referendum.
In a letter to The Sunday Telegraph, the Conservative associations said Mr Cameron had “undermined” the goodwill that existed among loyal members and warned him: “No prime minister has a divine right to rule.”
The missive was signed by 44 chairmen, executives, former chairmen and Tory activists, representing 43 local party associations across England, Wales, Scotland and Northern Ireland.
A Downing Street spokesman told the newspaper: “The PM has the greatest of respect for Conservative associations across the country.
“He was simply making the point that everyone should ultimately vote with their conscience.”
One of Margaret Thatcher’s former advisers, Lord Powell of Bayswater, suggested in an article for The Sunday Times that his former boss would have backed the current deal to stay in the EU.