The Labour Party leader was next in line to face the veteran BBC host and said he would not follow Theresa May down the road of pledging to lower immigration figures.
Mrs May, twice as Home Secretary and once as Prime Minister, has said she would lower net migration to the tens of thousands, something Mr Corbyn refused to match.
Mr Corbyn has previously said a Labour government would deliver a “fair” immigration policy and recognised it will “probably be lower”, adding he did not want to make predictions.
Neil insisted Mr Corbyn and Labour were not the party to fulfil some voters demands to lower the migration number.
Jeremy Corbyn refused to make a Labour Party pledge to lower immigration
Theresa May promised in three elections to cut immigration – I am making no promises on that
Mr Corbyn responded: “We are in favour of managed immigration when the free movement ends when we leave the European Union.
“We are against people being brought in as wholesale workforces to undermine existing working conditions and workers.
“There will be managed migration in the future based on…
However, Neil interjected: “Will you be cutting immigration?”
Mr Corbyn replied: “Based on the economic needs of our society.
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“We’ve had Theresa May promising in three elections to make cuts to immigration – I am making no promises on that.”
He said Labour would deal with immigration based on the “economic needs of the country as a whole” and to facilitate “necessary family reunions”.
Asked once against if he would try to cut the numbers, the Labour leader added: “Well, if the economy is doing well and we train people properly then the need to bring in skilled workers from overseas will obviously reduce.”
Mr Corbyn was also put on the spot over claims he has met with the IRA and his links to the group.
Snap election 2017: The pictures politicians may not want you to see Sat, May 27, 2017
Protests, fights and daleks, it's all happening as the politicians hit the campaign trail for the snap election
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Jeremy Corbyn during a visit to Hackney Marshes Football Pitches, to highlight Labour's manifesto commitment to ensure 5% of the Premier League's television rights income is diverted to the grassroots game, during a General Election campaign
He stressed his desire for peace in Northern Ireland, adding: “I never met the IRA.”
Asked why people would want him as prime minister given his previous support for the group, Mr Corbyn replied: “I didn’t support the IRA. I don’t support the IRA.
“What I want everywhere is a peace process. What I want everywhere is decency and human rights.
“We went through all the horrors of Northern Ireland – all through the 70s and 80s – through the period of the Troubles, and eventually came from that a peace process, the Good Friday Agreement, and now relative peace and stability."