The UK could suspend visas from countries that do not “play ball” and agree to returns deals for migrants, the new home secretary has said.

Shabana Mahmood made the comments as she hosted Donald Trump’s head of homeland security and ministers from Australia, New Zealand and Canada at a meeting of the intelligence-sharing Five Eyes group in London on Monday.

The talks came as the government continued to face pressure to reduce the number of people crossing the Channel in small boats.

Saturday, which was Mahmood’s first full day in the job, saw 1,097 people arriving, one of the highest number of people on record.

Speaking for the first time since being appointed on Friday, Mahmood said her “top priority” is “securing” the UK’s borders.

On visas, she said: “We think there is interesting space for collaborating, particularly on how we deal with countries who do not take their citizens back – so making sure we are able to return out of our countries people who have no right to be in our countries and send them back to their home countries.

“For countries that do not play ball, we have been talking about taking much more coordinated action between the Five Eyes countries.

“And for us that means the possibility of cutting visas in the future to say we do expect countries to play ball, play by the rules and if one of your citizens has no right to be in our country, you have to take them back.”

The home secretary did not specify which countries could be included in any future visa suspensions.

Sir Keir Starmer has previously said he favoured a “much more transactional” approach on visas.

In June, the prime minister said he was considering whether British visas could be granted depending on how well countries co-operate with the UK on issues such as taking back failed asylum seekers.

On Monday, the prime minister’s spokesman said an agreement among Five Eyes allies to cooperate over illegal migration provides “another tool in our armoury” and “shows our determination to use every lever at our disposal to crack down on illegal migration, to return people with no right to be here”.

Saturday’s small boat numbers brought the total number of people arriving in the UK by small boat to more than 30,000 this year, according to Home Office statistics, a number that Mahmood described as “utterly unacceptable”.

The number of people arriving in the UK by small boats this year is up by 37% on last year, according to analysis by the PA news agency.

Dr Madeleine Sumption, director of Oxford University’s Migration Observatory, said there were “quite a few countries where returns of refused asylum seekers are low and demand for UK visas is also high” – citing India, Bangladesh, Pakistan or Nepal as examples.

“How these countries would respond to threats to reduce visa access might depend how much they care about visa options for their citizens,” she said.

“This will vary, although some countries – such as India – have a long history of lobbying for visa access.”

Responding to the announcement, shadow home secretary Chris Philp said it was “about time this Labour government now stopped talking tough and started acting tough”, and said the UK should also cut aid to countries not taking back its citizens.

“This Labour government is too weak to take the steps necessary to protect our borders and I see no sign of that changing any time soon,” the Conservative MP added.

Mahmood held talks with US Homeland Security Secretary Kristi Noem, who oversees the US Immigration and Customs Enforcement (ICE) agency and has been a key player in the Trump administration’s efforts to ramp up deportations.

The Five Eyes alliance is a decades-old intelligence-sharing pact between the US, UK, Canada, Australia and New Zealand. It is often described as being among the most successful agreements between allies for sharing classified intelligence.

Online child sexual abuse and the spread of opioids were also on the agenda at the summit, which was attended by Canadian public safety minister Gary Anandasangaree, Australian home affairs minister Tony Burke and New Zealand minister Judith Collins.

Earlier on Monday, Mahmood said she hoped to agree new measures to “protect our borders with our Five Eyes partners, hitting people smugglers hard”.

Mahmood, formerly the justice secretary, was appointed as home secretary in the prime minister’s major cabinet reshuffle over the weekend, replacing Yvette Cooper.

Her appointment has been interpreted as Starmer seeking to send a clearer signal that dealing with illegal immigration and asylum is one of the government’s biggest priorities, given Mahmood has a reputation within Labour of being a hardliner on the issue.

On Sunday, Defence Secretary John Healey confirmed the government is looking at expanding the use of military sites to house asylum seekers, as it looks to move people out of asylum hotels.

He said officials were also considering other types of “non-military accommodation”.