A total of 509 people crossed the English Channel in 10 boats on the day six died when a boat carrying migrants sank off the coast of France.

The latest Home Office figures take the provisional total for the past three days alone to more than 1,600, with more than 16,600 having made the journey so far this year.

A Cabinet minister defended the Government’s immigration strategy on Sunday amid renewed pressure, including from Tory MPs, over its “stop the boats” pledge following Saturday’s fatal incident.

At least six people died and at least 58 – many of them Afghans – were rescued after a boat got into difficulty of the coast of Sangatte on Saturday.

According to the accounts of survivors, around 65 people had originally boarded the overloaded vessel before a passing ship saw it sinking and raised the alarm at around 4.20am.

Wales Secretary David TC Davis admitted the crossings would “continue to be a problem”, but insisted some boats were being stopped.

“We have stopped a lot,” he told Sky News.

Rishi Sunak has made tackling the crossings one of five key priorities for his leadership and asked people to judge him on his management of the problem.

MPs have called for action against criminal people-smuggling gangs profiting from the journeys while campaigners have described the deaths as an “appalling and preventable tragedy”.

Writing in the Sunday Express, Conservative backbencher and former party chairman Sir Jake Berry said: “We must put a stop to the vile people smugglers who trade in human misery and whose actions result in the loss of life.”

Meanwhile, shadow home secretary Yvette Cooper said action to deter criminal gangs facilitating the journeys is “desperately” needed.

Care4Calais said the incident was an “appalling and preventable tragedy”, while the Refugee Council warned “more people will die” unless more safe routes to the UK are created.

Home Secretary Suella Braverman described the incident as a “tragic loss of life” and said she had chaired a meeting with Border Force officials later on Saturday.

It comes after the Government was accused of allowing its “small boats week” of linked announcements on immigration to descend into farce following the removal of dozens of asylum seekers from the Bibby Stockholm barge.

Senior Conservative backbencher David Davis said the “startling incompetence” of the Home Office had been laid bare after all 39 people on board the 500-capacity vessel were disembarked due to the discovery of Legionella bacteria in the water supply.

However, ministers intend to push on with plans to hire more barges to house asylum seekers, as well as student halls and former office blocks, The Telegraph reported.

The people who had been on the Bibby Stockholm, which had been billed as a cheaper alternative to expensive hotels for those awaiting the outcome of their claims, are now back being housed in other accommodation.

The Home Office has said the health and welfare of asylum seekers “remains of the utmost priority” and that the evacuation took place as a precautionary measure, with all protocol and advice followed.

Minister David TC Davies on Sunday defended the Government’s handling of the setback, saying its evacuation of people from the vessel “actually demonstrates how we’re putting the safety of people first”.

Asked whether the incident points to a wider failure within the Home Office, he told Times Radio: “No, it doesn’t. It doesn’t at all. The checks were being made.”

But shadow education secretary Bridget Phillipson said a “better, fairer system” is needed to tackle the backlog of asylum applications and cut the need for temporary accommodation.

She told the same programme that prosecutions of people smugglers are “falling” under the current Government.

Without the French actually intercepting and detaining those boats, then we have a problem stopping that

Conservative MP Tim Loughton said the Government’s “small boats week” of linked announcements on immigration was a “hostage to fortune”.

He told Times Radio: “I think it was probably not a good idea to have a small boats week. It was a hostage to fortune and clearly it depends on how many people are risking their lives coming across the Channel, which is dependent on the weather and how people smugglers are operating.”

But Mr Loughton, a member of the Commons Home Affairs Select Committee, also said part of the problem lies with France, calling on the country’s authorities to intervene.

“Without the French actually intercepting and detaining those boats, then we have a problem stopping that,” he said.

“Secondly, the Home Office has got to do a lot better in speeding up the processing times of those people who do then come to the UK to see whether they have a legitimate asylum claim or not.”

Sir Iain Duncan Smith told the Mail on Sunday the incident was a “wake-up call for all those who speak only of rights, but seem incapable of balancing those rights against the terrible risks that people are undertaking”.