New legislation pledged by Rishi Sunak to tackle illegal migration will form only one part of the government’s response to the issue, a senior minister has said.

It comes as Home Secretary Suella Braverman is set to publish long-promised legislation as soon as Tuesday that would make asylum claims inadmissible from those who travel to the UK on small boats.

Sunak on Sunday vowed to put an end to “immoral” illegal migration, while Braverman said “enough is enough”.

But while details are still scarce on the legislation, critics have already questioned whether the government’s solution will make any difference to small boat arrivals on Britain’s shores.

The legislation would see a duty placed on the Home Secretary to remove “as soon as reasonably practicable” anyone who arrives on a small boat, either to Rwanda or a “safe third country”.

Arrivals will also be prevented from claiming asylum while in the UK, with plans also to ban them from returning once removed.

During an appearance on BBC One’s Sunday With Laura Kuenssberg, Northern Ireland Secretary Chris Heaton-Harris was shown a graph displaying a fall in asylum seeker returns since 2010 as he insisted that legislation is just one aspect of the Government’s “arsenal” on the issue.

“We need a full range of things in our arsenal to try and stop both people trafficking and illegal migration across the Channel,” he said.

“That involves proper conversations, that are ongoing, with our French counterparts, and indeed other European counterparts, to try and ensure that people are held in the first safe country that they come to. That also includes international development aid.”

He insisted a tightening of the law is required “because the law has been challenged on pretty much all those occasions and equally when we announced the Rwanda scheme, it was challenged immediately”.

The Prime Minister, who has made “stopping the boats” one of his five priorities, told the Mail on Sunday that he is “determined to deliver” on his promise.

But the Government’s plans have been criticised by campaigners, with concerns too about whether some of the policies are compatible with the European Convention on Human Rights.

The Rwanda scheme has been mired in legal challenges, and so far no flights carrying migrants to the Rwandan capital Kigali have departed.

The latest Home Office figures show 2,950 migrants have crossed the Channel already this year.

Heaton-Harris, speaking to Sophy Ridge On Sunday on Sky News, signalled that the Government may look at opening more “safe and legal routes” for asylum seekers in the future.

“I’m quite sure there’ll be more safe and legal routes and that’s why we have them,” he said. “They’ve been proven to work.”

Labour’s Jonathan Ashworth, speaking on Sky News, said his party would “study” the legislation carefully to see if it addresses the current issues, including processing backlogs.

Pressed on whether his party supports the “broad principle” behind the legislation, the shadow work and pensions secretary said: “The broad principle is that refugees who arrive in this country, we have always welcomed them.

“People whose asylum applications have been turned down, then of course they should be returned, that is a principle that we have always accepted.

“The problem is, of course, that the Conservatives will come out here and they will get headlines and they will say they are going to do this, that and the other, but they never deliver, do they?”

The Liberal Democrats called it “another half-baked plan”. The party’s home affairs spokesman Alistair Carmichael said it is “immoral, ineffective and incredibly costly for taxpayers”.