Conservative MPs are urging ministers to send people travelling to the UK by small boats to offshore centres as far away as the Falkland Islands as concern grows that the party is losing support among red wall voters. Priti Patel, the home secretary, should also be willing to automatically return migrants to France if the party is to fulfil the Brexit promise of taking control of the UK’s borders, MPs said. The increasingly extreme demands come amid deepening alarm in Downing Street and the Conservative party over the rising numbers of people risking their lives by making the journey in winter. High-ranking officials believe at least 10 people have died in the last few weeks while trying to make the crossing across one of the world’s busiest shipping channels. More than 1,000 have crossed in a single day twice in the past fortnight. Labour accused Patel on Sunday of “comprehensively failing” to curb the growing numbers of people taking the dangerous journey across the Channel. Downing Street’s concerns over the Channel crossings spilled into the public domain on Friday when Boris Johnson announced a review of the government’s small boats policies. The Guardian spoke to six Tory MPs from so-called red wall and Kent constituencies on Sunday. They are demanding that the government goes further in laying down hardline policies to deter people from entering the UK. Lee Anderson, the MP for Ashfield in Nottinghamshire, said he lobbied an immigration minister two weeks ago to say that offshore processing, where those who seek asylum are sent abroad while their cases are processed, should begin as soon as possible. “I would be in favour of [using] the Falkland Islands. The only way we will put these people off is by giving them the message that if you come here you are going to be sent 8,000 miles away,” he said. Craig Mackinlay, the MP for South Thanet, said he and his backbench colleagues are facing increasing demands via email and social media for the government to stop boats carrying migrants from entering the UK. “We had a Brexit election where one of the main issues was getting control of our borders. This is of massive concern to my constituency and many of our voters across the UK,” he said. He said the government should consider sending people straight back to France “although this could have diplomatic, high octane consequences”, he added. “In the long term, we should also be more involved in patrolling the French coastline. If advanced economies can’t successfully patrol 100 miles, using the technology we now have, it doesn’t say much and I frankly don’t believe it,” he said. Another MP said that Patel, who has said on 11 occasions that she will curb the number of boats crossing the Channel, has fallen into Johnson’s habit of overpromising and underdelivering on a key government policy. “Voters will see through this government. HS2, social care and migrant boats – it is difficult not to see a pattern and it has to stop,” the MP said. Hundreds more people, including very young children, have made the dangerous Channel crossing to the UK over the weekend. Adults carrying youngsters and others wrapped in blankets were seen arriving on the south-east coast of England on Saturday with help from lifeboat crews. More than 24,700 people have arrived in the UK so far this year after making the Channel crossing in small boats – almost three times the number in 2020. Appearing on the Andrew Marr show, Labour’s shadow home secretary, Nick Thomas-Symonds, said Patel was “comprehensively failing” to stem the flow. “It appears the prime minister agrees because he seems to be putting the minister for the Cabinet Office in charge of a review of this,” he said. Downing Street sources said Steve Barclay has been brought in to ensure that different departments are working together to solve the small boats issue. Enver Solomon, chief executive of the Refugee Council, said the government faces a serious challenge if it is to deliver on its promise to control the UK’s borders. “It needs to stop overpromising and underdelivering, recognise it’s a complex issue that requires less meaningless rhetoric and more intelligent realism, less harsh control and more human compassion.” Minnie Rahman, the interim chief executive of the Joint Council for the Welfare of Immigrants, said MPs are treating refugees like a political football. “The reason we’ve been seeing more dangerous crossings is because government has closed down or limited practically every safe route for people seeking protection. “The only way government will end dangerous crossings is by taking practical, evidenced-based steps like providing safe, regulated means of travel for people seeking protection.” Claims also emerged in the Mail on Sunday that Patel has become so frustrated by the obstructions of officials and legal advisers that she has considered writing to the cabinet secretary, Simon Case, to list her department’s failings. Dave Penman, the head of the FDA union, told the Guardian it was “unedifying” to see under-pressure ministers resort to briefing against their own staff. “If ministers are genuinely interested in solving this crisis, they should be concentrating on working with their civil servants rather than wasting time briefing the Sunday papers in a transparent and desperate bid to shift blame,” he said. Sajid Javid, the health secretary, defended the government’s efforts to solve the crisis in the Channel and said Covid had made things more difficult. “We do need new agreements with countries, predominately with the countries where most of the failed asylum seekers are coming from, and those aren’t always European countries, and this home secretary has done that, she has signed new agreements and put those in place with countries like India. “But also I would say that the pandemic has made returning people across the world, across asylum systems, much harder, and we do have to take that into account as well,” he said.