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By Andre Rhoden-Paul
BBC News
Ministers are facing renewed pressure to tackle boat crossings in the Channel after six migrants died when a vessel sank off the French coast on Saturday.
Labour urged the government to end the "small boats nightmare", while a Tory backbencher said the UK had a "moral duty to act".
The government has made "stopping the boats" one of its five priorities.
Investigations continue into Saturday's incident in which 59 people were rescued and two may still be missing.
The overloaded vessel, which got into difficulty and capsized 12 miles (20km) off Sangatte, was said to be one of a number of migrant vessels which set off on Saturday in the hope of reaching the UK.
Labour's shadow immigration minister Stephen Kinnock accused the government of having "no workable plan" to sort out the asylum system.
"It's time to end the small boats nightmare - we can't sit by as more lives are put at risk. The country deserves better than this mess," he wrote in the Sunday Mirror.
Mr Kinnock suggested a Labour government would negotiate a returns agreement with the EU and go after smuggling gangs by a creating a new cross-border police unit.
Calls for action have also come from within the Conservative Party. Backbench MP and ex-party chairman Sir Jake Berry said "only radical changes can truly turn the tide".
Writing in the Sunday Express, he said: "We have a moral duty, both to our own citizens and those asylum seekers, to act."
Refugee charity 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, who chaired a meeting with UK Border Force officials on Saturday, said the deaths were a "tragic loss of life".
The new Illegal Migration Bill, spearheaded by Ms Braverman, is central to the government's plans to stop small boats crossing the Channel. It places a legal duty on the home secretary to detain and remove anyone entering the UK illegally.
The government is also planning a new agreement with France, under which the UK will pay £500m over three years to fund more patrol officers and a new detention centre.
French authorities said the migrant boat was first detected by a commercial vessel, before a French patrol boat was dispatched to the boat in distress.
French sea minister Hervé Berville said: "While we mourn these victims ... it is the responsibility of human traffickers - of criminals - who send young people, women, adults, to their death on these maritime routes that are dangerous and lethal."
Investigators are looking for any information that might lead them to the smuggling gang which organised the crossing.
According to rescued migrants, 65 or 66 migrants had been on board the boat.
One of the volunteer rescuers told the Reuters news agency migrants were using shoes to bail water out of the sinking boat.
A search for two people who may still missing has been called off, pending new information coming to light.
Many of the migrants on board are believed to have come from Afghanistan, and others from Sudan. It also understood children were among them.
Aid workers in Calais have told the BBC's Bethany Bell more migrants have been arriving in recent weeks and have been living rough on the coastlines. They say many of them are determined to get to the UK, despite warnings over the dangers of the crossing.
French authorities said they rescued another 59 people onboard a boat near Calais on Saturday, before bringing them to Dunkirk.
The pressure on the ministers follows criticism after 39 asylum seekers had to be moved off the Bibby Stockholm barge due to the discovery of Legionella bacteria in the water supply.