In the wake of the London Bridge terror attack, Mr Corbyn called on Theresa May to resign as Prime Minister for presiding over police cuts while Home Secretary.
The BBC’s Daily Politics host, however, blasted Mr Dromey, insisting his party’s leader would be in no better position to protect Britain from terror.
Mr Dromey had already criticised the Conservative Government for failing to protect the public from a Khuram Butt, one of the three London Bridge attackers, who was known to the authorities for his link to terrorists, including one of the 7/7 Tube bombers.
Coburn berated the Labour politician claiming Mr Corbyn “wouldn’t have locked up” the would-be terrorists from Manchester and London, who were known to authorities before they launched their attacks.
Jack Dromey was taken apart by Jo Coburn over Jeremy Corbyn's anti-terror stance
Jeremy Corbyn has proudly voted against 17 separate anti-terrorism laws
She said: “Jeremy Corbyn has proudly voted against 17 separate anti-terrorism laws over the course of his career.
“He called for Hamas to be removed from the list of prescribed terror groups and said Britons shouldn’t be banned from returning from fighting for ISIS.
“When people look at that record, they will say under Labour and Jeremy Corbyn nothing would have been done about Khuram Butt.”
During a speech in 2014, Mr Corbyn questioned the “legal obstacles” for fighters returning to the UK from Syria.
Asked by a Conservative MP if he believed ISIS fighters should be subject to special measures, Mr Corbyn suggested they should not be prosecuted for “expressing a political point of view”.
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He said: “I have no support for ISIS whatsoever, and obviously that should apply to someone who has committed crimes, but we should bear in mind that express a political point of view is not in itself an offence.
“The commission of a criminal act is clearly a different matter, but expressing a point of view, even an unpalatable one, is sometimes quite important in a democracy.”
London terror raids Sun, June 4, 2017
Police have raided a block of flats in Barking in connection with last night's London Bridge terror attack.
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As police continue their investigations following the June 3 terror attacks, a block of flats in Barking is raided for possible suspects
Referring to those comments, Coburn added: “He would not have locked up the people involved in this offence!”
Mr Dromey diverted attention away from the question, claiming instead voters want to see more police on the streets and the rebuilding of neighbourhood policing.
He concluded: “I think what we’ve got to do is to focus, right now, on what’s crucial, a great national unity to oppose and defeat terrorism.
“And then it is about the powers necessary and the resources to do it.”