The clip, shared by a Twitter user who described themselves as a “defender of British democracy”, has been viewed more than 870,000 times. The BBC has been coming under increasing pressure over the past few months with the Government suggesting it could decriminalise non-payment of the licence fee.
Tim Davie, its new director general, has said the corporation needs to “recommit to impartiality”.
The viral video was from an episode of BBC Question Time filmed earlier this year in Weymouth.
Mr Portillo, who has presented a number of programmes for the BBC, argued the licence fee doesn’t have a long-term future.
He said: “I have to begin by declaring an interest because I derive most of my income from the licence payer and therefore you might be surprised when I say I do not believe the licence fee can survive.
“It’s partially actually my experience of making films.
“I make films with very young people and the young people with whom I make films do not pay the licence fee.
“They do not have televisions. They consume their media on their mobile phones or their laptops.
“They don’t even watch the programmes they make with me because they have no access to the BBC. The BBC is losing its audience.”
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“I don’t think there’s much evidence on the BBC that they’re doing things that other people could not possibly do.
“For example there’s almost no arts programming on BBC television.
“Twenty years ago the BBC was a global name. Today the BBC is wedded to the licence fee.
“It is like a polar bear on a receding piece of ice.”
New BBC director general Tim Davie has pledged to crack down on corporation stars airing their personal opinions on social media.
He commented: “If you want to be an opinionated columnist or a partisan campaigner on social media then that is a valid choice, but you should not be working at the BBC.
“We urgently need to champion and recommit to impartiality.
“In the age of fake news, social media campaigns, echo chambers of opinion, and noisy partisan media outlets, this, surely, is our time.”
It is currently illegal to watch live television in the UK without having a TV licence.
A standard licence costs £157.50 per year and those who watch without paying risk large fines.