In an exchange around the validity of the result of the election, Ferrari drew Burnham into commenting on the due diligence undertaken towards those seeking to join the Labour party as supporters or affiliates.
Ferrari asked Burnham: "How confident are you about that due diligence?"
Ferrari pointed to his membership email on a laptop during the exchange
"Yeah I'm confident in it, Nick," Burnham said, "I've raised concerns along the way. Yes we have confidence in the result come Saturday."
As the interview continued, Ferrari explained that he had received a vote in the election, despite his Conservative affiliation being well documented.
He told Burnham: "You would not have known this, but I applied to have a vote. I applied, and I have here in front of me my eight digit security code and I have my code part two that starts with a letter and then a number.
"I applied, and you only have to go on my Wikipedia page, and it's a grim thing to do to go on my Wikipedia page, but the third item on there is that I met with David Cameron to become the Conservative Mayor of London before Boris Johnson arrived.
Burnham stumbled before saying: "I don't know Nick, because I've not been running this process."
"It's a shambles isn't it? It has to end now?" Ferrari asked, before continuing, "This robustness, this due diligence - it's a sham.
"You can't even stop people getting into your own voting system"
The results of the leadership election will be declared on Saturday.
360,000 people have joined the party as supporters or affiliates.