Claire Enders, a London-based media analyst who is a friend of Mr. Davie’s, said he once told her that his job at the BBC was like opening a Pandora’s box stuffed with unpleasant surprises, every day.

“Every director general has faced these issues,” she said, “but he has faced more of them because, during his tenure, the world has become much more divided.”

“They made a mistake, and when they discovered it, they didn’t own up to it,” Ms. Enders said. “What’s best for the BBC is to have a reset and address these issues. For the BBC to manifest political bias is the most dangerous thing it could do in this world.”

“What’s best for the BBC is to have a reset and address these issues,” said Claire Enders, a media analyst in London. “For the BBC to manifest political bias is the most dangerous thing it could do in this world.”

Claire Enders, of Enders Analysis, said: 'It would be a transformative move by Sky and ITV and it would potentially be a very good fit. It is a daring and very brave move.'

But she suggested it may take 18 months to reach an agreement and get the deal past regulators, with the combined company having a 70 per cent share of the TV advertising market.

Tom Harrington at Enders Analysis says: “There certainly could be remedies, but there is a growing acceptance that the market needs greater collaboration and efficiency to stay resilient – this will aid the argument for consolidation.”

While there is crossover between the ITV audience and Sky subscribers, Tom Harrington, Head of Television at Enders Analysis, said the broader audience will be a much better sell to advertisers. “You’d be enormous in a shrinking market,” he added. “If you have a declining business in many ways and combine it with another [declining] business then suddenly you look a lot bigger. That is better, even if putting them together won’t really arrest what they are facing.”

Tom Harrington, from Enders Analysis, said: "It would be unlikely for current shows to leave ITV as there will already be agreements in place."

But splitting the two businesses could make it less likely for new shows to appear on ITV, he added.

Mr Harrington said ITV Studios itself was a "very desirable operation" that was "unencumbered by a legacy linear [TV] business".

Media analyst Claire Enders said a long regulatory process was likely but that a deal would strengthen both public service broadcasters and prolong the mass advertising market.

Gill Hind, managing director and director of TV at Enders Analysis, suggested this could particularly impact streaming.

She told the PA news agency: "ITVX is growing but is still behind iPlayer and Channel 4 in terms of how many of the channels’ viewers use the streaming service.

“There could definitely be streamlining crossover opportunities with Sky able to make their programmes available to ITVX users who wouldn’t usually access their shows." She added that sports coverage could also see shared rights across public and paid-for channels.