It was hoped a deal could be reached which would allow Britain to return asylum seekers to the first EU country they arrived in.
French President Emmanuel Macron suggested this could be agreed if Brexit Britain accepted legal routes for asylum seekers trying to enter the UK and if it allowed for unaccompanied minors to join family members who have arrived here already.
However, a deal now seems unlikely given disputes between countries over migration policy, according to The Times.
There is a lot of disagreement between EU countries over how to divide the number of refugees in different countries fairly.
Italy has threatened to veto a migration deal between Britain and the EU until agreements are reached on migrant policy reforms.
A diplomatic source defended Italy’s “perfectly rational” position, saying: “It would be bizarre to be helping Brexit Britain when the EU cannot agree on solidarity for Italy.”
Another source said: “The EU will not do a deal to help ease the pressure on Britain’s border, which is tiny compared to what is faced by many Europeans, while member states are still divided on burden sharing themselves.”
There has reportedly been “no tangible progress” since the issue was first raised by Macron in November last year.
A Government source added : “Everyone wants burden sharing until they have to share the burden themselves.
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The Home Office has said the Government wants to impose tougher asylum rules.
However, refugee charities have slammed this as a “dangerous and callous policy”.
Clare Moseley, founder of charity Care4Calais, said: “They are some of the most vulnerable people in the world, having lost family members in bloody conflicts, suffered horrific torture and inhumane persecution.
“The Government tells us people should travel by legal means, but if this were truly possible why would so many be risking their lives in flimsy boats?”