Kemi Badenoch has promised to do “whatever it takes to deal with the small boats issue” as she pitched controlling immigration at the centre of her campaign for the Tory leadership.

It came with the former equalities minister in fourth place but many MPs believing she is well-placed to pick up votes in the third round on Monday, having impressed many activists with her performances so far in the contest.

The MP for Saffron Walden outlined a focus on property ownership, border control and family as the “first, and best, source of welfare” as herself and the four other contenders still in the contest prepare for the second televised debate to be screened on ITV on Sunday evening.

“Property ownership should be spread as widely as possible. Nations need borders. The family is the first, and best, source of welfare,” she wrote in The Sunday Times.

“People – rightly – recognise that building more homes while doing nothing to bring immigration down is like running up the down escalator,” she added.

“We’ll never get to where we need to with that approach, and we won’t persuade people to accept more homes if it is being done due to immigration failures. If we can bring immigration down to a sustainable level, we can then protect green spaces for our children and precious agricultural land.

“And so controlling immigration is important to managing the pressures it puts on housing and public services. Building confidence in the Government’s ability to control immigration is an important foundation for ensuring a cohesive society.”

More than 14,000 migrants have made the 20-mile journey across the Channel so far this year, navigating the world’s busiest shipping lanes from France in small boats like dinghies, provisional Government figures show. The total for 2022 is anticipated to be 60,000.

Home Secretary Priti Patel in April signed a deal to send some migrants to Rwanda, however legal challenges have stopped any departures.

Former equalities minister Ms Badenoch said it was her belief in Britain’s sovereignity that led her to vote Leave in the Brexit referendum.

“I am a firm believer that we must control our own borders and laws. I will do whatever it takes to deal with the small boats issue,” she wrote on Sunday.

“I am not someone who starts fights to get headlines – and I want to focus on the people’s top priority, which is the economy. But economic issues around housing and immigration are inextricably linked.

“As is the link with the family. Family break-ups increase housing demand, and the unaffordability of housing in many areas stops people establishing the family life they want. Family is the first line of welfare, and strong families reduce the need for a larger state.”

Ms Badenoch vowed to “look at how our tax and benefit system can support family life and the joys it brings”, adding: “Coherent, Conservative conviction leadership is what I will bring if you elect me as prime minister.”

Her pitch came as leadership frontrunner Rishi Sunak tried to win over Brexiteers by pledging to scrap hundreds of remaining EU laws and regulations if he wins the race.

International trade minister Penny Mordaunt remains in second place, Foreign Secretary Liz Truss is third and backbencher Tom Tugendhat sits in fifth.