Boris Johnson has called on France to agree to joint patrols across the Channel after a migrant boat capsized and 27 people died.
The Prime Minister said the tragic incident - which involved the deaths of several men, five women, one who was reportedly pregnant, and a little girl - showed the operations that have taken place to date 'haven’t been enough'.
He said the French haven't worked to stop the dangerous journeys being made despite £54 million of UK support.
However the mayor of Calais, Natacha Bouchart, said that it was the British who were to blame.
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She called 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.
The French regional maritime authority has now confirmed that 27 people died in the incident, which happened on a 'very frail boat' likened to a 'pool you blow up in your garden'.
French officials had previously stated there were 31 deaths but the death toll was revised down.
Two survivors are said to have been picked up during the rescue operation, which was launched after a fishing boat spotted people in the sea off Calais.
The survivors are being treated in a French hospital.
Boris Johnson spoke to President Emmanuel Macron on Wednesday evening.
He said he wanted to work with the French authorities to 'demolish' the business model of human traffickers who were 'literally getting away with murder'.
"We’ve had difficulties persuading some of our partners, particularly the French, to do things in a way that we think the situation deserves," Mr Johnson 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."
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", he told BBC2’s Newsnight.
"That is something that I am very keen to see happen.
"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.”
Mr Johnson 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.
French interior minister Gerald Darmani insisted the French authorities wanted to work with the UK to tackle the issue.
After speaking to Home Secretary Priti Patel earlier this week, he said he had sent a list of further assistance they required.
“We have to work together. Sadly our differences with legislation sometimes mean there is a slight lack of co-operation,” he said.
Ultimately it required a tough co-ordinated international response if they were to be effective, Mr Darmanin said.
“This can only be done if Belgium, Germany, Holland, the UK, work all together. Possibly we are not working together enough yet,” he said.
“We really must fight against these criminals just as we fight against terrorism.”
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.
