The United States and the United Kingdom are taking sweeping efforts to crack down on asylum claims by migrants who have entered their country illegally – as their leaders face political pressure over ongoing migrant crises.

"If you enter Britain illegally, you will be detained and swiftly removed," U.K. Home Secretary Suella Braverman said in the House of Commons on Tuesday.

Braverman was announcing new legislation, the "Illegal Migration Bill," which will block asylum claims for any migrant who enters the U.K. illegally. The bill sets out how they will be detained or quickly returned to a home country or a third country. The government has previously made a safe third-country agreement with Rwanda.

Britain has struggled for decades with migrants who enter Europe and move across the continent before reaching France and attempting to cross the English Channel either by stowing away on vehicles or by crossing the water in small boats.

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Braverman UK migrant crisis

Home Secretary Suella Braverman speaks in the House of Commons on the" Illegal Migration Bill," March 7, 2023.

Those coming to the U.K. by small boat shot up from 8,500 in 2020 to 28,000 in 2021 and 45,000 in 2022, raising considerable pressure on the government as backlogs increase and hotels become overcrowded with housed migrants. Repeated Conservative governments have promised, and largely failed, to crack down on illegal immigration.

Prime Minister Rishi Sunak said the consequences of a no-asylum policy would lead to reduced traffic.

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"People must know that coming here illegally will result in their detention and swift removal – once they do, they will not come, and the boats will stop" he said.

The U.K. announcement is similar in many ways to the announcement last month by the Biden administration of a proposed rule to crack down on asylum claims at the southern border. Under the rule, migrants would be automatically presumed to be ineligible for asylum if they have crossed into the U.S. illegally and have failed to claim asylum in a country through which they have already traveled.

Unaccompanied children would be exempt, and there would be other factors that could rebut the presumption, including an acute medical emergency, being a trafficking victim, and facing an "extreme and imminent" threat to life or safety. But all others would be presumed to be ineligible and therefore removable.

Migrants can still claim asylum, but they must present themselves at a port of entry and schedule an appointment on the CBP One app. The rule is set to go into effect in May, ahead of the end of the Title 42 public health order.

That comes as the administration continues to deal with a migrant crisis now into its third year, with more than 2.3 million migrant encounters in FY 2022 and an FY 2023 on track to outpace those numbers. The administration has said that recent numbers that show a sharp drop in encounters are proof that the administration's policies are working.

The move has been attacked by left-wing Democrats and immigration activists who have compared it to a Trump-era transit ban. The administration has rejected that narrative, saying that it is opening up asylum pathways, which migrants need to use. 

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DHS Secretary Alejandro Mayorkas

Department of Homeland Security Secretary Alejandro Mayorkas (Drew Angerer / Getty Images)

"As we have seen time and time again, individuals who are provided a safe, orderly, and lawful path to the United States are less likely to risk their lives traversing thousands of miles in the hands of ruthless smugglers, only to arrive at our southern border and face the legal consequences of unlawful entry," Homeland Security Secretary Alejandro Mayorkas said in a statement announcing the rule.

But that has done little to blunt the left-wing pushback. The American Civil Liberties Union has threatened to sue if the rule is finalized. Meanwhile, Rep. Lou Correa, D-Calif., called the move "unconscionable, unacceptable, and un-American."

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A coalition of Democratic senators said the move "perpetuates the harmful myth that asylum seekers are a threat to this nation" as they called on the administration to reverse course.

There has been a similar left-wing pushback in the U.K., with activists and Labour politicians claiming that the legislation is unworkable and cruel. The bill is also likely to face considerable legal challenges in the coming months.

Shadow Home Secretary Yvette Cooper called the bill a "con that makes chaos worse" and accused her Tory rivals of "government by gimmick."

The Associated Press contributed to this report.