Nearly all women who try to reach the UK in small boats from northern France have been raped on their journey, Shabana Mahmood has claimed.

In an interview with The Rest Is Politics podcast, the home secretary said far-right, balaclava-wearing activists would “kill” or “kick me out of my own country” if they took power.

Speaking to the former Tory minister Rory Stewart and Tony Blair’s former close adviser Alastair Campbell, she said sexual abusers would exploit most asylum seekers as long as traffickers continued to decide who came to the UK.

She said: “We’re not in control of this border. The sifting of the people that end up in the north of France and are about to get on a dinghy is done by criminal gangs who are also, by the way, people traffickers.

“You can almost guarantee that every woman that’s in the north of France has probably been raped along the journey. Some of the men too, they’ve certainly been abused and threatened. That is not the model that should decide whether somebody gets to come to the UK, make this their place of sanctuary and ultimately become one of us.”

Asked by Campbell about balaclava-wearing protesters shutting down ports and praising her policies, she said they should “sod off”.

She added: “They’re just troublemakers. You know, they’d kill me in a minute if they could, and they’d definitely kick me out of my own country. So let’s just be really clear about who and what they are. They don’t think I’m a true Brit and they hate the fact that I’m a Muslim.”

Mahmood also said she considered herself “part of the pro-Palestinian cause” and felt “very uncomfortable” over the arrests of activists opposing the ban imposed on Palestine Action.

Merseyside police arrested 82 people on Monday at the Labour party conference on suspicion of wearing or carrying articles supporting a proscribed organisation.

In a protest organised by Defend Our Juries, scores of people sat outside the conference centre in Liverpool, many holding handmade banners saying they supported Palestine Action.

Mahmood said: “For those of us who have been in the pro-Palestinian cause all of our lives, these are people – sometimes you’ll know who they are, you know, you’ve been on the marches with them – it feels very uncomfortable to see them falling foul of section 13 of the Terrorism Act.”

However, she defended enforcing the ban, regardless of her views: “You’ve got to be able to apply your principles, even when it’s uncomfortable for you, because you’re going to really want to apply them when it’s something you, you know, with your whole heart, are feeling very passionately about.”

Authorities were preparing on Sunday for the arrival of a migrant dinghy heading for the south coast. The boat was being shadowed by French coastguard and rescue vessels and moving toward the Channel boundary line, according to ship tracking data.

It appeared to have set off from near the Utah Beach area of Normandy on Sunday morning.

Caroline Dinenage, the Conservative MP for Gosport in Hampshire, said there was “nothing to suggest” the boat would land on the county’s coast but police were “making preparations should that situation change”.

A government spokesperson said: “The Border Security Command works around the clock to monitor the Channel and protect our border. It is vital we continue to detain, check and process every small boat arrival.”

Imran Hussain, a director at the Refugee Council, welcomed the home secretary’s acknowledgment of widespread sexual violence, but questioned why the government had closed safe and legal routes which could help asylum seekers avoid falling into the hands of predators.

“We know from our services that women and girls fleeing war and persecution face sexual violence both in the conflicts they have escaped and on the journeys they are forced to make in search of safety,” he said.

“That is why in welcoming the government’s announcement last week of new safe routes we called for them not to be limited to a few hundred people. Last year the government closed family reunion, the safe route for refugees which overwhelmingly benefits women and children.

“It is entirely right to talk about the dangers women face on these journeys but we should not be closing the safe routes that could keep them out of harm’s way. Protecting women means more safe routes, not fewer.”