An activist investor with a $5bn-plus stake in 21st Century Fox has told the board it must ignore the personal benefit Rupert Murdoch may enjoy from a deal with Disney and fairly evaluate Comcast’s $60bn (£45bn) bid.

TCI, which is run by Sir Christopher Hohn, has steadily built up a 7.4% stake in Fox which has a market capitalisation of $72bn.

Activist Hohn, the son of a Jamaican car mechanic who emigrated to Britain in the 1960s, has written a letter urging the board of Fox to “immediately engage” with Comcast.

On Wednesday, Comcast confirmed that it is preparing to top Disney’s $52bn (£39bn) bid for Fox, which owns assets including the Hollywood studio 20th Century Fox, which makes films including X-Men and Deadpool, and a 39% stake in Sky.

Comcast put in a $60bn bid for Fox last year, a 16% premium to Disney’s offer, but Murdoch rejected the offer, citing regulatory concerns and share structure. The Murdochs, who control Fox through voting shares, will receive about 5% of Disney if that deal goes through.

“We are aware that the Murdoch family has a potential conflict of interest because of capital gains tax, which could lead them to preferring a lower priced Disney stock offer, to a higher priced offer from Comcast,” said the letter from Hohn. “However, the personal tax position of the Murdoch family must be an irrelevant consideration for the board, in order for the board to comply with their fiduciary duties.”

He added that the board must run a “fair auction” and “sell to the highest bidder”.

Comcast, which is also mounting a separate £22bn bid to take control of Sky, said it is in the “advanced stages” of preparing an all-cash offer for the entertainment and broadcast assets that Fox has agreed to sell to Disney.

“Comcast Corporation confirms that it is considering, and is in advanced stages of preparing, an offer for the businesses that Fox has agreed to sell to Disney,” the company said.

“Any offer for Fox would be all-cash and at a premium to the value of the current all-share offer from Disney. The structure and terms of any offer by Comcast … would be at least as favourable to Fox shareholders as the Disney offer.”

Comcast, which owns NBC Universal, said it had not made a final decision on whether to make a formal offer but that the work on financing a bid and making regulatory findings were “well advanced”.

It is understood that any bid for Fox, which does not include assets such as Fox News and Fox Sports which are being spun-off separately by the Murdochs, will have no impact on Comcast’s bid for Sky. A Comcast deal for Fox, which controls 39% of Sky, would complete well after a deal for Sky.

A spokesman for Fox declined to comment on the potential Comcast bid. However, at the company’s recent results Lachlan Murdoch, Fox’s executive chairman, was asked about reports of Comcast considering gatecrashing the Disney deal.

“We are committed to our agreement with Disney and are working through the conditions to bring it to a closing,” he said. “In addition, our directors, though, of course are aware of their fiduciary duties on behalf of all shareholders.”

Daniel Ives, head of technology research at GBH Insights, said that a Comcast bid would be “game changing” and, if successful, would seriously harm Disney’s plan to build and provide content for a rival streaming service to Netflix.

“In our opinion [the deal] is integral to the streaming ambitions of [Bob] Iger [Disney chief executive] and Disney,” said Ives. “With Comcast already going after Sky assets in Europe, this would be a logical and aggressive move to go after these golden entertainment assets of Fox and would move Comcast to the forefront of the streaming game potentially over the coming years.”

Earlier this week, Comcast’s bid for Sky was given a boost when the culture secretary said he was “minded not” to refer it to broadcasting regulator Ofcom to assess any potential public interest concerns.

Murdoch’s bid for the 61% of Sky that he does not already own is still being assessed by Hancock. The culture secretary has until 13 June to decide whether to clear or block the deal, having received a report from the Competition and Markets Authority at the beginning of the month.

Sky’s independent board, which had told shareholders to accept Murdoch’s offer, withdrew that recommendation in light of Comcast’s higher bid.

Fox has said it remained committed to its offer for Sky and is “considering its options”, which means it could potentially raise its bid.