Labour has urged the government to speed up the process of deporting failed asylum seekers and criticised "12 years of Tory failure" in the immigration system.
Rachel Reeves, the shadow chancellor, said the government needed to clear a backlog removals aimed at people "who have not got a right to be here".
Suella Braverman, the home secretary, said on Tuesday that she would ban people arriving in the UK unlawfully from applying for asylum – likely to be a breach of UN refugee treaties.
Ms Braverman, who also said she dreamed of overseeing a successful Rwanda deportation flight, was branded "shameful, cruel and senseless" by charity the Joint Council for the Welfare of Immigrants (JCWI).
Asked whether she welcomed the Home Secretary's plan to ban the asylum claims, Labour's Ms Reeves told Sky News:
"The problem is the government are not deporting people today, even when their claims have failed.
"What the government need to do is get a grip of the system, process claims quicker, and ensure people who have not got a right to be here are sent home.
"That is not happening today and that is 12 years of Tory failure."
She added: “The Conservatives have been in government for 12 years now and illegal immigration is on the increase, so this is a problem that's been made under their watch.
“They need to process claims faster and get people out of the country if they've got no right to be here and get a grip of their failed immigration system, which is not working for British people and its not working for genuine asylum seekers either.”
Ms Reeves's comments provoked a backlash inside Labour, with the shadow chancellor accused of "throwing migrants under the bus".
Labour For Free Movement, a migrants' rights pressure group within the party, said Ms Reeves' comments were "politically misguided, morally inexcusable".
"Labour can’t win by trying to out-Tory the Tories and out-racist the racists," a spokesperson for the group said.
"This only shifts the debate to the right - at a time when we’re way ahead in the polls and public opinion on immigration is increasingly positive. Reeves is throwing migrants under the bus for nothing."
People wanting to claim asylum in the UK have few options to do so because there is often no legal means for them to arrive in Britain – so thousands have taken to crossing the Channel by small boat, with more than 33,500 using the route so far this year.
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The vast majority of people crossing by boat, 94 per cent according to government statistics, end up applying for asylum – with only a minority of claims unsuccessful.
Ms Braverman's proposal would ban those people from claiming asylum in the first place, without providing an alternative route to do so – despite the fact the Home Office accepts them as genuine refugees.
Speeding up asylum decisions is part of Labour’s five-point plan to reduce the number of people crossing the channel in small boats.
The party says it would work with France, Belgium and Interpol to crack down on criminal smuggling gangs – redirecting spending from the government’s Rwanda policy to create a new team at the National Crime Agency.
It would also seek to negotiate a replacement for the Dublin agreement and reform resettlement schemes to prioritise those with family connections in the UK.