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.”

The home secretary said the bill will mean last-minute judicial reviews “conducted late at night with no chance to make our case or even appeal decisions” are no longer allowed.

“Our approach is robust and novel, which is why we can’t make a definitive statement of compatibility under section 19 1b of the Human Rights Act,” she added.

“Of course, the UK will always seek to uphold international law and I am confident that this bill is compatible with international obligations.”

Under the proposed plan:

• It will be possible to detain people for 28 days without bail or judicial review

• The onus to remove those who enter illegally will be on the home secretary – to “radically” narrow the number of challenges and appeals

• Only those under 18, those medically unfit to fly or at “real risk” if they are returned to the country they have left will be able to lodge an appeal to stop them from being deported

• Any other claims will be heard remotely after they have been removed

• People will be prevented from using modern slavery laws to oppose the government

• An annual cap on the number of people entering via safe routes – to be set by parliament – will “ensure an orderly system”.

Ms Braverman added that the government is adding to its detention capacity, including on military bases.

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”.