Corbyn’s announcement in his flagship speech at the Labour conference could spark rows with his MPs who are calling on him to put a target on the number of people who will be allowed in.
But the Labour leader insists he will not make “false promises”, and a look at the immigration commitments from the Tory government over the last few years suggests that may be a good idea.
Promises to reduce immigration have rarely worked out - just look at this long line of blunders under David Cameron and Theresa May’s governments:
The fateful promise
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In 2012 David Cameron stated in the Tory election manifesto that he would “take steps to take net migration back to the levels of the 1990s – tens of thousands a year, not hundreds of thousands.”
The commitment to get net migration below 100,000 was one he would doggedly hang on to despite there being pretty much no evidence to suggest it was achievable.
Ignoring the evidence
Cameron's former policy guru Steve Hilton claims the PM was "directly and explicitly" told by civil servants that his pledge would fail if Britain stayed in the EU. This warning came less than a year after the manifesto promise, Hilton claims, and made it clear that the target was "impossible" to achieve.
Promise? What promise?
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In 2014 Cameron downgraded the 100,000 target to an “ambition” rather than a promise, after net migration fell but then rose again. "It’s clear it’s going to take more time,” he said.
The Vote Leave website said: "More than a quarter of a million people came to the UK from the EU in the 12 months to September 2015 – the equivalent of a city the size of Plymouth or Newcastle."
In January a think tank called Cameron's migrant promise "effectively dead", the Guardian reported. British Future said his plan to reduce migrant access to welfare benefits would have little benefit and urged him to admit this... he ignored them.
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Vote Leave also attacked Cameron's "impossible" pledge during the EU Referendum campaign, with its chair, Labour MP Gisela Stuart, saying a promise to control numbers that couldn't be kept was "corrosive" of public trust in politicians.
The Leave campaign changes tune
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But Vote Leave's own promise that leaving the EU was the only way to "control" EU immigration has rather fallen flat too.
Nigel Farage, who was not part of the official campaign but called for Britain to leave, said: "Mass immigration is still hopelessly out of control and set to get worse if we remain inside the EU."
But according to a BBC 'Reality Check' report, these campaigners have changed their tune since the vote. They now claim immigration levels "can't be radically reduced by leaving the EU" and that fears about immigration did not influence the way people voted, the BBC reports.
BBC Reality Check notes this contradiction, saying: "Some Leave campaigners sent a clear message that the referendum was about controlling immigration... Vote Leave's focus on it was a key part of their strategy."
Rock and a hard place
Cameron's dodgy promise leaves Theresa May in a tough spot. As the new PM, she "can’t throw every inherited policy pledge out of the window – especially when she was the Cabinet Minister in charge of the policy area," writes Mark Littlewood in the Daily Mail.
But the "foolish" commitment she may have to stick to "epitomises all the worst elements of modern British policy-making," he says. "It’s overly specific, attention-grabbing, unenforceable nonsense, littered with negative economic consequences and doomed to lead to increased anger and disillusionment among the voting public."
Getting a bit vague
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It's possible that the target may be scrapped, though not as quietly as the Government might like. In July, the new Home Secretary Amber Rudd suggested the Government wasn't keen on explicit targets, saying its "aim" is to reduce net migration to “sustainable levels”. She didn't specify what "sustainable" meant.
Even Boris thinks it's a bad idea
Even Foreign Secretary Boris Johnson seems to back the target being dropped, saying in July that it was right to be "careful" about committing to numbers "because one doesn't want to be in a position where you are disappointing people again”.
We won't admit we need migrants
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"Worse than the foolish promise is the fact that politicians haven't taken any steps to cut the immigration that was within their control, because we know we need migration," writes Littlewood.
"To appreciate the absurdity, you only have to look at the net migration figures for 2015. Out of the total of more than 300,000 migrants, around half came from outside the EU – meaning we already had the power to cut that back if we had chosen to. But we didn’t. We needed them.
"It would be a con trick on the British people to pretend net immigration levels can ever fall to some specific number without us suffering profound economic damage.
"We need immigrant labour. Those of us who backed Brexit but believed that immigration can be an enormously positive force always understood that. Those who just wanted to wave around absurd targets and numbers on immigration really do have to wake up to economic reality."
“The country’s voted to come out of the EU and the biggest single issue in that was ending freedom of movement to bring the numbers down for those coming here," he said in the Telegraph.
"Despite what Rudd and Johnson have said, he insisted the idea of dropping the target is 'a non-starter'. It would fly in the face of what the referendum was about. It would be absurd if we broke our pledge on that. It wouldn’t happen and can’t happen."