Boris Johnson has called on France to agree to joint police patrols along the French Channel coast after a migrant boat capsized causing the loss of dozens of lives.
The French regional maritime authority said 27 people had died. French officials had previously stated there were 31 deaths but the death toll was revised down, with no immediate explanation for the discrepancy.
The British Prime Minister spoke to President Emmanuel Macron on Wednesday evening in the wake of the worst incident of its kind in the Channel since the current migrant crisis began.
Downing Street said they had agreed to "keep all options on the table" in their efforts to break up the human trafficking gangs responsible for putting desperate people at risk in one of the world's busiest sea lanes.
Immigration compliance minister Tom Pursglove confirmed that Mr Johnson had renewed a previous offer to send UK police and Border Force officers to mount joint patrols with the French.
The aim is to prevent migrant boats from attempting the perilous crossing but the French have previously resisted amid concerns about the implications for their national sovereignty.
Mr Pursglove said, however, the last incident showed the two countries needed to deepen their co-operation in dealing with the issue.
"The Prime Minister and President Macron have had exactly that discussion this evening. That is something that I am very keen to see happen," he told BBC2's Newsnight.
"It is the case that in the past we have offered to host and to help with joint patrols. I think that could be invaluable in helping to address this issue. I really do hope that the French will reconsider that offer."
There was shock and dismay on both sides of the Channel at what was widely described as a "tragedy".
A joint search and rescue operation by the French and British authorities launched after a fishing boat spotted people in the sea off France was finally called off late on Wednesday.
French interior minister Gerald Darmanin said the dead included five women and a girl while two survivors had been picked up and were being treated in a French hospital. One of the dead women was later reported to have been pregnant.
Mr Darmanin said the boat the which sank had been very flimsy, likening it to "a pool you blow up in your garden".
The French authorities have arrested four suspected people traffickers in connection with the incident while the regional prosecutor has opened an investigation into aggravated manslaughter.
Following a meeting of the Cobra emergencies committee, Mr Johnson said it was clear that French operations to stop the migrant boats leaving "haven't been enough" despite £54 million of UK support.
He said the people traffickers were "literally getting away with murder" and that he hoped the French would now find the renewed offer of joint patrols "acceptable".
"We've had difficulties persuading some of our partners, particularly the French, to do things in a way that we think the situation deserves," he said.
"I understand the difficulties that all countries face, but what we want now is to do more together - and that's the offer we are making."
However the mayor of Calais, Natacha Bouchart, said that it was the British who were to blame and called on on Mr Johnson to "face up to his responsibilities".
"The British Government is to blame. I believe that Boris Johnson has, for the past year and a half, cynically chosen to blame France," she said, according to French media reports.
Mr Johnson, meanwhile, said the Government would seek to "accelerate" measures in the Nationality and Borders Bill to enable the authorities to "distinguish between people who come here legally and people who come here illegally".
But Enver Solomon, chief executive of the Refugee Council, said the incident should lead the Government to rethink its approach.
"Surely a tragedy of this magnitude is the wake up call our Government needs to change its approach and finally commit to an expansion of safe routes for those men, women and children in desperate need of protection," he said.
The president of the French voluntary rescue organisation the Societe Nationale de Sauvetage en Mer in Calais said more cross-Channel human trafficking could be expected.
Bernard Baron told FrancInfo radio: "It's very shocking to see victims like today and it's not over since we're having an exceptionally calm month of November. November is usually stormy."
He added that smugglers would likely continue trafficking in the coming weeks.
Maya Konforti, secretary general of the French humanitarian organisation l'Auberge des Migrants, said the sinking of the migrant boat in the Channel was a "catastrophe".
She told French TV channel BFMTV: "We were sure this would happen one day, but up 'till now... when there have been deaths, it was one or two at a time, but this is a catastrophe."
She said the NGO was working to identify the bodies, contact the families, organise the funerals and repatriate the bodies.
"When it's one or two people it's manageable, but with 31 people, we don't know how we're going to do it. It will be very, very complicated and it will also be very, very expensive."
She added the British Government and French interior minister were blaming smugglers, but "the existence of smugglers is in response to a need; a need because there's no legal way to go and seek asylum in Britain".