Labour leadership candidate Yvette Cooper has called for Britain to open its doors to more refugees from Syria, arguing it should be possible to take some 10,000 people seeking asylum.

The shadow home secretary said the failure to offer sanctuary to people trying to escape the "new totalitarianism" of Islamic State (IS) was "immoral" and "cowardly", and urged the Government to exclude refugees from its target to reduce net migration below 100,000 a year.

Her call came as Nigel Farage warned of "an exodus of biblical proportions", with millions of people crossing the Mediterranean in the hope of making a better life in Europe.

The Ukip leader said Britain should offer refugee status to "a few thousand people" from Syria but should follow Austria's lead in imposing much tighter checks at borders to prevent illegal immigration.

He told BBC Radio 4's Today programme that the EU's common asylum policy had "potentially... opened the door to an exodus of biblical proportions, meaning millions and millions of people".

With anyone fleeing war or extreme poverty able to claim asylum in Europe, "we've lost sight of what is a genuine refugee", he said. "How many millions does Europe want to take? That really is the question."

In a speech to the Centre for European Reform in London, Ms Cooper said the Mediterranean crisis was a test of the values professed by Britain and Europe, and both had so far been "found wanting".

"This has become a humanitarian crisis on a scale we have not seen on our continent since the Second World War. Yet we seem paralysed to respond," she said.

"We can't carry on like this. It's immoral, it's cowardly and it's not the British way."

Ms Cooper contrasted Britain's offer to take a few hundred Syrian refugees to the Kindertransport programme of the 1930s, when in a matter of months it accepted 10,000 Jewish children fleeing the Nazis.

And she called on the Government to summon a national conference to determine how many places can be offered to refugees from Syria and the Mediterranean.

"If every city took 10 refugee families, if every London borough took 10 families, if every county council took 10 families, if Scotland, Wales and every English region played their part, then in a month we'd have nearly 10,000 more places for vulnerable refugees fleeing danger, seeking safety," said Ms Cooper.

Ms Cooper's demand for action was backed by the other three leadership candidates in a hustings hosted by Channel 4 News.

None would put a figure on how many refugees Britain should take, but Jeremy Corbyn said it should be "a considerable number", while Liz Kendall said the country could welcome "thousands more".

"I think there has to be a coming together of European countries, recognising there is a crisis and we've all got to play our part," said Mr Corbyn.

Andy Burnham said the Government could win support for Britain's demands for reform to EU freedom of movement rules by showing leadership on the refugee issue.

"Where have they been all summer? Where have they been as this crisis has been unfolding across the continent?" he asked. "This could be a moment for Britain to show leadership so that we can get changes elsewhere in terms of immigration policy."

Ms Kendall said: "David Cameron should be asking local councils what they are able to do and putting that forward across Europe as part of a negotiation, because we have to do more than we are doing at the moment."

David Cameron's official spokeswoman told reporters: "The UK has a proud history of providing refuge to those in need and we should continue to do so, while also tackling illegal economic migration."

But a home affairs spokesman for Angela Merkel's CDU/CSU in Germany - which has said it expects to receive 800,000 asylum seekers this year - indicated that patience was wearing thin with Britain's refusal to open its doors.

"There is not much understanding for the British attitude of saying `We are not willing to take more refugees and asylum seekers'," Stephan Mayer told Radio 4's World At One.

"I would say a lot of European member countries should take more refugees and asylum seekers, and also Great Britain - as a big country, the third biggest country in the European Union - should take a bigger proportion of the big challenge we have now to tackle in the European Union."

A European Commission spokesman said: "EU rules on asylum are a translation of international law, the Geneva Convention - we do not turn people away whose lives would be endangered should they be sent back, people who have no place to go.

"At the same time people who do not have a right to stay in Europe need to be sent back.

"The European Commission put on the table in May a comprehensive plan which includes as one of its main pillars increasing the rate of effective returns.

"There are EU rules on returning irregular migrants and the European Commission will work to ensure they are effectively applied."