The legislation, promised as part of Government efforts to tackle illegal migration, could come as soon as Tuesday, as Home Secretary Suella Braverman said that the only way into the UK would be a “safe and legal route”.
The legislation is expected to make asylum claims inadmissible from those who travel to the UK on small boats.
It would see a duty placed on the Home Secretary to remove “as soon as reasonably practicable” anyone who arrives on a small boat 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.
Campaigners have already hit out at the “vindictive” proposals.
The bill will be published on Tuesday, according to The Sun on Sunday.
Ms Braverman told the paper: “Enough is enough. The British people want this solved.
“They are sick of tough talk and inadequate action. We must stop the boats.
“That’s why myself and the Prime Minister have been working flat out to bring forward necessary and effective laws which will tackle this problem, once and for all.
“It has to be that if you come here illegally you will be detained and swiftly removed.
“Our laws will be simple in their intention and practice – the only route to the UK will be a safe and legal route.”
It has to be that if you come here illegally you will be detained and swiftly removed
Home Secretary Suella Braverman
The Prime Minister has made “stopping the boats” one of his five priorities, while Ms Braverman has repeatedly promised to take a hard line on illegal migration and Channel crossings.
But the Government’s plans have also 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 too 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.
Mr Sunak has been under considerable pressure from his own backbenches to tackle illegal migration.
Downing Street has said that the legislation will come in due course.
Critics expressed concern at the plans.
This legislation will do nothing to reduce the number of deaths in the Channel or the chaos and incompetence that blights our asylum system
Sonya Sceats, Freedom from Torture
Christina Marriott, executive director of strategy at the Red Cross, called it “extremely concerning”.
“The Home Office knows from its own research that this will also do little to prevent people risking their lives to seek safety.
“Again and again, we hear from people that they have no prior knowledge of the UK’s asylum system, so making it harsher is not an effective strategy,” she said.
Sonya Sceats, chief executive at Freedom from Torture, called the proposals “vindictive and dysfunctional”.
“This legislation will do nothing to reduce the number of deaths in the Channel or the chaos and incompetence that blights our asylum system, nor will it guarantee sanctuary for those who need it.
“Instead, it will lead to more torture survivors being unfairly denied protection and potentially removed to Rwanda.”