Refugee charities have also described the plans as "costly and unworkable" and said they "promise nothing but more demonisation and punishment" of asylum seekers.

Home Secretary Suella Braverman is set to publish long-promised legislation on people crossing the Channel on small boats on Tuesday.

Follow politics live - New legislation expected to be revealed Tuesday

A ban on people who come to the UK illegally from claiming asylum is believed to be among the proposals being put forward in a new Illegal Migration Bill.

Michelle Donelan, science, innovation and technology secretary, told Sky News' Kay Burley at Breakfast programme on Monday: "The basic principle will be that if you travel here illegally, then it's not okay to stay."

She added that many people arriving on small boats are travelling "across many safe countries to get here...and if they're travelling here illegally they shouldn't be allowed to stay".

Government minister Chris Heaton-Harris said on Sunday the legislation will ensure people who come to the UK illegally "are returned very quickly" or to another country such as Rwanda.

Rishi Sunak has made stopping Channel migrant crossings one of his five priorities in office, promising to introduce new laws to "make sure that if you come to this country illegally, you are detained and swiftly removed".

Several Tory MPs welcomed the news that a new bill was imminent, but the plans have been criticised by opposition parties, with Labour accusing the government of "recycling the same rhetoric and failure" and the Liberal Democrats saying ministers had drawn up "another half-baked plan".

Enver Solomon, chief executive of the Refugee Council, said plans to deny those crossing in small boats the ability to claim asylum would "shatter the UK's long-standing commitment under the UN Convention to give people a fair hearing regardless of the path they have taken to reach our shores" and would "add more cost and chaos to the system".

Steve Valdez-Symonds, Amnesty International UK's refugee and migrant rights director, said the government's proposals "promise nothing but more demonisation and punishment of people fleeing conflict and persecution who dare to seek asylum in the UK by means to which government has chosen to restrict them".

Sonia Sceats, chief executive of Freedom from Torture, accused the government of having "comprehensively shut down" legal routes for refugees to come to the UK and said the legislation "would place a bomb" under the cardinal principle of refugee law - that those genuinely fearing for their lives should be able to reach a country by any means possible.

Mr Sunak on Sunday vowed to put an end to "immoral" illegal migration. Speaking to the Sunday Express, he said: "Illegal migration is not fair on British taxpayers, it is not fair on those who come here legally and it is not right that criminal gangs should be allowed to continue their immoral trade."

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A report in The Sunday Times said the Home Office had drawn up two plans to stop people arriving via small boats from claiming asylum - either withdrawing the right to appeal against automatic exclusion from the asylum system, or only allowing them to appeal after they have been deported.

A third proposal would prevent people from using the Human Rights Act to prevent their deportations, such as by claiming their right to family life.

The legislation could also 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".

Cabinet minister Chris Heaton-Harris told Sky News' Sophy Ridge On Sunday programme that the new laws would be "very black and white" and "safe and legal routes are certainly the way forward".

However, questions have been raised about how any such legislation, based on the details known so far, could be compatible with the European Convention on Human Rights.

The government's previous Rwanda scheme became mired in legal challenges, with so far no flights carrying migrants to the Rwandan capital Kigali departing.

The latest Home Office figures show 2,950 migrants have crossed the Channel already this year, while a record 45,756 migrants were recorded to have arrived in the UK last year.

A Home Office spokesperson said: "The home secretary has been clear that if you arrive in the UK illegally, you should not be allowed to stay.

"We will shortly introduce legislation which will ensure that people arriving in the UK illegally are detained and promptly returned to their home country or a safe third country.

"Our work with France is also vital to tackling the unacceptable rise in dangerous Channel crossings. We share a determination to tackle this issue together, head-on, to stop the boats."