The home secretary has announced a new illegal migration bill that will mean migrants arriving on small boats will be “removed swiftly”.

Suella Braverman told the Commons: “They will not stop coming here until the world knows that if you enter Britain illegally you will be detained and swiftly removed back to your country, if it is safe, or a safe third country such as Rwanda.

She told MPs she “can’t make a definitive statement of compatibility” of her legislation to halt small boat crossings of the Channel under the Human Rights Act.

The new Illegal Migration Bill will mean asylum claimants cannot use modern slavery laws to block their removal, the home secretary said.

Claims for asylum can be made after they have been removed and that can only be delayed for a few exceptions, including for those under 18 years old, medically unfit to fly or at real risk of coming to harm in the country they are removed to.

Ahead of the announcement, the home secretary said the plan “pushes the boundaries of international law” but insisted it is needed because the asylum system is being “overwhelmed”.

Former justice secretary Sir Robert Buckland told Sky News on Tuesday morning he had been assured the bill would not actually break international law.

The prime minister had said the new bill, which is key to one of his five priorities, will “take back control of our borders, once and for all”.

Opposition parties and refugee charities had already started criticising the bill before it was announced, with some saying the plans were “costly and unworkable” and they “promise nothing but more demonisation and punishment of asylum seekers”.

Critics said the UK had “comprehensively shut down” legal routes for refugees to come to the UK.

Labour raised doubts about the legality and feasibility of the bill and the Liberal Democrats said ministers had drawn up “another half-baked plan”.

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