Downing Street spent Thursday scrambling to match public outrage and calls for Britain to do more to alleviate the human cost of Europe’s gravest post-war migration crisis, which were led by the Archbishop of Canterbury.

The grieving father of Aylan Kurdi spoke of the harrowing image of his lifeless son lying face down on a beach. “We want the world to see this,” Abdullah Kurdi said.

He described the moment that he lost his entire family. “I was holding my wife’s hands. My children slipped from my hands. We tried to hold on to the boat but it deflated rapidly. Everyone was screaming,” he said, as he left the mortuary that held the bodies of Aylan, his brother Galip and the boys’ mother.

“I could not hear the voices of my children and my wife. I tried to swim to the beach by following the lights. I looked for my wife and children on the beach but couldn’t find them.”

Aides said that Mr Cameron had not seen the photographs when he said on Wednesday that the crisis would not be solved by accepting “more and more refugees”.

Their publication — and the reaction of the public — forced Downing Street into full-scale retreat, senior government figures acknowledged. Signalling the change, the prime minister said that he had felt “deeply moved” by the image of the dead boy and that Britain would accept its “moral obligations”.

With London Mayor Boris Johnson and the party’s Scottish leader Ruth Davidson among a growing number of Conservative figures publicly calling for a rethink, Mr Cameron also faced pressure from cabinet colleagues.

Justine Greening, the international development secretary, and Nicky Morgan, the education secretary, each pushed for more action behind the scenes. Ms Greening urged the Prime Minister to approve increased funding for camps, now expected imminently, while Ms Morgan counselled a change of strategy and tone to meet the shifting public mood.

“You know you’re in the wrong place when the debate is being led by the Labour leadership candidates,” a Conservative source said.

It is understood that Mr Cameron’s favoured option is for Britain to increase the numbers that it takes from camps along the Syrian border.

Wider use of the Vulnerable Persons Relocation Scheme would enable him to say that Britain was taking those judged by the United Nations to be the most needy victims of the conflict, while continuing to hold out against European Union pressure to accept a quota of those already in Europe.

Only 216 people have been accepted into the Home Office scheme and previously ministers have resisted calls to increase the total above “several hundred over three years”.

The Times has learnt that the European Commission wants to relocate 160,000 asylum-seekers from Hungary, Italy and Greece across the EU with binding quotas.

Senior government officials say that Mr Cameron remains determined to avoid measures that he believes could encourage more people to risk the journey into Europe from the Middle East and Africa.

Divisions within Europe became yet more rancorous when Hungary’s Prime Minister warned that Europe was in danger of being overrun by Muslims. Viktor Orban dismissed the crisis as a “German problem” and defended his new razor wire border fence as essential to preserve Europe’s Christian heritage.

Donald Tusk, the president of the European council, took Mr Orban to task, saying that “referring to Christianity in a public debate on migration must mean [showing] ... humanity to our brothers”.

In Britain the Most Reverend Justin Welby, the Archbishop of Canterbury, said: “We cannot turn our backs on this crisis. We must respond with compassion.”

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