The audience member said: “Like many voters I approve of the policies in your manifesto, the problem I have don’t see you as someone who can effectively run this country.
“How can you convince me that you are someone that can effectively run this country?"
Mr Corbyn appeared to avoid the question initially as TV interview Jeremy Paxman had to force the Labour leader to answer the question.
Jeremy Corbyn was quizzed about whether he could be trusted
The Labour leader responded: “But you know what in life you meet lots of people, some I agree with some I profoundly disagree with.
"But I always want to get to know them.”
Challenged by one man who said he liked the Labour manifesto but did not see Mr Corbyn as "someone who could run this country", the Labour leader said he saw himself as a listening politician.
He added: "You should never be so high and mighty you can't listen to somebody else and learn something from them.
"Leadership is as much about using this (gesturing to his ear) as using this (pointing to his mouth)."
Jeremy Corbyn in pictures Tue, July 12, 2016
Labour Leader Jeremy Corbyn takes part in a community meeting at the Guru Har Rai Gurdwara Sahib temple
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Britain's opposition Labour Party leader Jeremy Corbyn speaks at an anti-racism rally in London
Mr Corbyn also said that he accepted the result of the Brexit referendum and that Britain would be leaving the EU.
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He said: "We accept the result of the referendum. It has happened, we accept it."
But he refused to be drawn on immigration levels after Brexit although he aid it would "probably" be no higher than at present.
"I am not going to stand here and put a figure. Our Prime Minister has done that now in the third election and got nowhere near meeting that figure.
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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
But you know what in life you meet lots of people, some I agree with some I profoundly disagree with
"I would have thought that under a managed migration system it certainly would not go up any more. It would probably – I don't want to be held to this – probably come down. It is a probability."
During the debate Mr Corbyn defended his comment that the killing of Osama bin Laden by US special forces had been a "tragedy".
"I think he should have been arrested and he should have been put on trial. And he could have been."
And defended his description of the Palestinian group Hamas as "friends".
Mr Corbyn said: "It was inclusive language at a meeting in which I was promoting the idea of a two-state solution, in which I was promoting the need for dialogue between Israel and all aspects of Palestine including Fatah as well as Hamas."