Prime Minister David Cameron is under growing pressure to show compassion towards Syrian refugees from British tabloids, opposition politicians and a few MPs from his own Conservative Party ranks.

A petition urging Britain to accept more refugees garnered over 100,000 signatures, while columnists urged Cameron to take action a day after he warned Britain taking "more and more refugees" would not help.

"Mr Cameron, Summer is Over... Now Deal With The Biggest Crisis Facing Europe Since WW2," read a headline in The Sun, Britain's top-selling daily, on Thursday next to a photo of a dead Syrian boy on a Turkish beach.

Several newspaper editorials harked back to the times when Britain accepted huge numbers of refugees in the aftermath of World War II and the Balkan Wars.

"We have done it before, and can do it again," Alan Travis wrote in The Guardian, while David Aaronovitch in The Times said the international community as a whole should "rediscover the humanity of 1945".

Contenders for the leadership of the main opposition Labour Party all urged Cameron to do more.

One of them, Yvette Cooper, has urged Britain to immediately accept 10,000 more Syrian refugees.

Tom Tugendhat, a Conservative MP from the Kent region in southeast England where some undocumented migrants arrive on ferries or through the Channel Tunnel, said: "Our common humanity demands action at home and abroad."

Britain has accepted 216 Syrian refugees under a special government scheme over the past year and around 5000 Syrians have been granted asylum over the past four years since the conflict there broke out in 2011.

More than four million of Syrians have fled the war.

Britain has also opted out of a quota system for relocating asylum seekers - a stance that is drawing growing criticism in other parts of Europe.

"It is clear that in front of this mess, in front of this particularly serious crisis, we would welcome that every country take on more responsibility," Italian European Affairs Minister Sandro Gozi told BBC Radio 4's Today program.

"When it comes to the UK, the UK has a special status but if you have a special status you cannot seek to shape policy in which you don't want to participate," he said.

Peter Sutherland, the UN special representative on international migration, said on BBC's Newsnight program that while some countries were "massively bearing the burden" of the migrant crisis, Britain was among those that "can do more".

"I think that this country can do more. The only way to solve this problem is by a united European response and that means sharing responsibility for appalling suffering," he said.

"This is a humanitarian crisis that Europe has not experienced in our time of a dimension which demands a common response.

"At the moment it is true to say that a number of countries are massively bearing the burden of this," he said, naming France, Germany, Italy and Sweden.