The home secretary has unveiled the 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.

“And that is precisely what this bill will do. That is how we will stop the boats.”

Small boats crackdown reaction – latest politics updates

The home secretary said the bill, which was formally introduced on Tuesday afternoon, 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.

She added that she “can’t say definitively” if the new bill complies with human rights laws.

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

On the first page of the published bill, a statement from Ms Braverman says: “I am unable to make a statement that, in my view, the provisions of the Illegal Migration Bill are compatible with the Convention rights, but the government nevertheless wishes the House to proceed with the bill.”

Under the proposed plan:

• People arriving on small boats will be detained within the first 28 days without bail or judicial review and can be detained after that if there is a reasonable prospect of removal

• 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” of serious harm in the country they are removed to will be able to lodge an appeal to stop them from being deported

• Any other claims, including the right to private or family life, will be heard remotely after they have been removed

• People will be prevented from using modern slavery laws to oppose their removal

• Deportation can only be deferred for modern slavery when a person is cooperating with law enforcement agencies in trafficking investigations

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

• A lifetime ban on settlement, citizenship and re-entry to the UK for those removed under the scheme.

The bill’s second reading, when it will be debated for the first time, will take place next Monday and the committee stage, where MPs go through the bill in detail, will be in the week starting 27 March.

Read more: Is there a safe and legal route to the UK?

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

She added that new safe routes have yet to be decided but said the bill will allow there to be a “more comprehensive discussion” on them to allow “more legitimacy” on what they should be.

The home secretary said the bill was “not about scapegoating, this is about safeguarding”.

She added: “It is essential that the UK takes a robust approach, but compassionate approach. This is, at core, a humanitarian package of measures which sends the message to people: do not come here illegally.”

Rishi Sunak, visiting a Home Office joint control centre in Dover after the announcement, said “we’ve got to somehow break the cycle of these criminal gangs” involved in trafficking people over the Channel in small boats.

Staff told him on busy days “we have to prioritise, we have to look in the boats and see if there are women and children in there”.

Labour: ‘Bill is a con’

Opposition MPs hit out at the plan, with Labour’s shadow home secretary Yvette Cooper calling the bill a “con” as she described the plans as “Groundhog Day”.

The veteran Labour MP mentioned a smuggler interviewed by Sky News the day before, saying the “disgraceful Tory attitude…is letting criminals off the hook and has let the gangs take hold”.

She added: “One smuggler told Sky News yesterday that three-quarters of the smugglers live in Britain, yet barely any of them are being prosecuted and they still haven’t found the hundreds of children missing from asylum hotels who have been picked up by criminal gangs.

“They could be setting out a serious plan today – and we would work with them, and so would everyone across the country.

“Instead, it’s just more chaos.”

Diane Abbott, who was Labour’s shadow home secretary under Jeremy Corbyn, accused Ms Braverman of using “inflammatory” language as she called the bill “deplorable and unworkable”.

In Ms Braverman’s original statement, she said: “For a government not to respond to waves of illegal migrants breaching our borders would be to betray the will of the people we were elected to serve.

“They will not stop coming here until the world knows that if you enter Britain illegally you will be detained and swiftly removed.”

‘Only 50% chance compatible with Human Rights Act’

Moments after the home secretary’s statement Conservative MPs and peers were sent a letter, seen by Sky News, by Ms Braverman, Immigration Minister Robert Jenrick and Home Office minister Lord Murray of Blidworth, urging them for their support for the bill.

It outlined the main details of the bill and insisted it “does not mean the provisions in the bill are incompatible” with the Human Rights Act.

“Only that there is a more 50% chance that they may not be,” the letter said.

“We are testing the limits but remain confident that this bill is compatible with international law.”

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”.