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Border Force officials rescued 49 migrants in the English Channel on Boxing Day.
Yesterday it was reported that at least 15 migrants had been brought to shore at Dover having crossed the channel in two small boats.
Authorities have now increased the figure and say the migrants crossed from France in four small boats.
More than 20 additional migrants are thought to have been intercepted by French authorities.
The coast guard PREMAR Manche Tweeted that 14 people, some with hypothermia, had been stopped in a dinghy off the coast of Boulogne-sur-Mer and included the below photo.
Bridget Chapman from Kent Refugee Action Network thinks the UK's planned departure from the EU could be a factor.
"I'm just extremely glad that everybody appears to have got over safely," she said. "It's an incredibly dangerous journey; the weather conditions this morning are not good, so I'm extremely relieved that everybody is safe.
"We're talking about the busiest shipping lane in the world. It's not easy at the best of times and in these conditions it is terrifyingly dangerous.
"I think that people are probably having pressure put on them by traffickers who are telling them that Brexit is going to happen and they are going to have to go now. Clearly that's an extremely dangerous thing to be telling people .
"We've worked with a number of people that have made this journey and everybody says they were terrified. They thought they were going to die - they were cold, they were wet, often they were hypothermic by the time they got here - just an awful journey to have to make.
"I worked with a young woman who made the crossing almost exactly a year ago on Christmas Day last year. She said it was rough, she was violently sick and she thought she was going to die - this is an incredible young woman who has made great progress in her studies here, and is going to be a fantastic asset to our county, I'm extremely glad that she's here safely."
She said most people that crossed from France have got extremely good asylum claims, and were keen to make themselves known to authorities, adding: "Our experience tells us that most of the people making this journey in dingies are Kurdish. They're from Iran or Iraq and for various reasons - sometimes persecution, sometimes the situation in Iraq, which is breaking down and becoming extremely violent - those people have been forced to leave their countries.
"I think we need to be clear that we're talking about relatively small numbers of people in terms of displaced numbers of people worldwide, and the relatively small number that are coming are usually coming because they have contacts here in the existing Kurdish community and they think they have the best chance of rebuilding their lives here."
But Tory MP for Dover Natalie Elphicke said those trying to get to the UK illegally from France should be returned.
“The people traffickers operate their illegal trade everyday of the year, including over the entire festive period from Christmas Day to New Year," she said. "The UK and the French authorities should be equally ready. In particular the French should be take firm action to stop these small craft setting off from the French coast.
“The weather was very mild on Christmas Day. These were perfect conditions for illegal departures from France. The French ought to have been more vigilant.
“Border force, the RNLI and HM Coastguard work tirelessly to save lives. But the truth is there should be an agreement between Britain and France that people who are found in the English Channel should be safely returned to France and not brought into Britain. That would be the best deterrent and the most effective way to bring this crisis to an end.”