British Prime Minister David Cameron is expected to draw up a plan on Friday as a response to growing pressure to accept Syrian refugees, thousands of them directly from UN camps on the border with Syria.
Cameron said he had been "deeply moved" by images of three-year-old Syrian toddler Aylan Kurdi, who was found dead on a Turkish beach and said Britain would meet its "moral responsibilities".
British newspapers reported that the outpouring of popular support for accepting more refugees had sent the government scrambling to come up with a response.
The Times and the Telegraph reported that a plan was being drawn up to accept "thousands" of refugees, with the option of directly accepting refugees from UN camps on the Syrian border under consideration.
"Final details of the numbers, funding and planned location are being urgently thrashed out in Whitehall," the Guardian cited government sources as saying.
"Cameron remains convinced that accepting large number of Syrian refugees who are already in Europe will make the crisis worse and encourage more chaos."
Without making specific commitments, Cameron on Thursday said Britain would keep the number of refugees it accepts "under review" although he added: "There isn't a solution that's simply about taking people, it's got to be a comprehensive solution".
"We do care," Cameron told reporters.
Britain has accepted 216 Syrian refugees under a special government scheme over the past year and around 5,000 Syrians have been granted asylum since the conflict there broke out in 2011 -- far fewer than countries like France, Germany and Sweden.
More than four million Syrians have fled the war.
Britain has also opted out of a quota system for relocating asylum seekers within the European Union despite growing calls in the EU for fairer distribution.
A petition to parliament urging Britain to accept more refugees has garnered over 325,000 signatures, while campaign group Avaaz said that 2,000 Britons had volunteered to host refugee families.
British newspaper front pages on Friday focused on the story of the little boy, Aylan, pictured dead on a Turkish beach in an image that became a powerful symbol of the refugee crisis.
"For Aylan" was the headline of The Sun, Britain's best-selling newspaper, with the subheading "How you can aid kids like tragic tot".
"They slipped from my hands" was the front page headline of the Daily Mail, which told of how Aylan's father had failed to stop his two sons and his wife from drowning.
On the streets of London, views on the issue varied.
"I can't believe that we haven't done anything before now," said 45-year-old Victoria Buurman as she walked with her shopping in central London.
"I think it's disgusting that we have to get to a point where children are dying before we even recognise that we're not acting morally. It's horrific," she said, breaking into tears.
But Souvik Ghosh, a 26-year-old research student from India, said Britain should not take any more migrants.
"There should be some limitations, OK? Because otherwise this country's economic system will be overflowed," he said.
Contenders for the leadership of the main opposition Labour Party have all urged Cameron to do more.
One of them, Yvette Cooper, has urged Britain to immediately accept 10,000 more Syrian refugees, while bookmakers' favourite Jeremy Corbyn added there was no "electric fence and military solution" to the crisis.
"It's a humanitarian crisis and it must be solved by human beings acting in a humanitarian way," he said.
Several MPs from Cameron's own Conservatives also urged the prime minister to do more.
"Our common humanity demands action at home and abroad," said Tom Tugendhat, who represents part of the Kent region where many undocumented migrants arrive on ferries or through the Channel Tunnel.
There was also criticism from elsewhere in Europe, with the Council of Europe's Commissioner for Human Rights, Nils Muiznieks, saying he was "seriously concerned" by Cameron's position.
"While it is true that long-term peace should be brought to Syria and other war-torn countries, it is also true that the UK has a legal and moral obligation to offer shelter to those who flee war and persecution," he said.
"The truth is that at the moment the UK is doing much less than other European countries".
Peter Sutherland, the UN special representative on international migration, told the BBC that while some countries were "massively bearing the burden" of the migrant crisis, Britain was among those that "can do more".