The resignations of the BBC’s director general and its head of news over claims of bias were “a coup” orchestrated from the inside, a former newspaper editor has claimed.

David Yelland, who edited the Sun from 1998 to 2003, told BBC Radio 4’s Today programme on Monday that the departures of Tim Davie and Deborah Turness followed the systematic undermining of them by people close to the BBC board over a lengthy period.

“It was a coup, and worse than that, it was an inside job. There were people inside the BBC, very close to the board … on the board, who have systematically undermined Tim Davie and his senior team over a period of [time] and this has been going on for a long time. What happened yesterday didn’t just happen in isolation,” Yelland, who also co-presents the BBC podcast When it Hits the Fan, said.

“What has happened here is there was a failure of governance. I don’t blame the chairman [Samir Shah] as an individual, but the job of the chair of any organisation, a company – including the BBC – is to keep their CEO, their top man or woman, in post or fire them. And that has not happened, because Tim Davie was not fired. He walked and so there was, that is the definition of, a failure of governance.”

The resignations on Sunday followed days of attacks from the White House and rightwing commentators in the UK that were prompted by claims published by the Daily Telegraph.

The paper reported a leaked record of the findings of a former independent external adviser to its editorial guidelines and standards committee, Michael Prescott, who left his role in the summer.

He had criticised the editing of a speech by Donald Trump in an edition of Panorama, which he claimed made it appear that Trump had encouraged the US Capitol attack. Two sections of the speech that were spliced together were made an hour apart, and the edit did not note that Trump had also said he wanted his supporters to demonstrate peacefully.

Yelland’s criticisms echo a mood of dismay described by sources within BBC News on Sunday night, with one saying: “It feels like a coup. This is the result of a campaign by political enemies of the BBC.”

Others, including Sky’s former political editor Adam Boulton, have said the overall impression that Trump egged on the insurrection was fundamentally true. It is not unusual practice to edit together sections of a long speech to accurately summarise it.

Davie said his departure would not be immediate and that he was “working through” timings to ensure an “orderly transition” over the coming months. Turness said controversy around the Panorama edit had “reached a stage where it is causing damage to the BBC – an institution that I love”.

On Monday, the BBC journalist Nick Robinson said there had been paralysis at the top of the BBC because, while its senior journalists wanted to apologise for the editing error – but insist there was “no intention to mislead” the audience – the politically appointed directors wanted to go further.

Shah is expected to apologise on Monday to the Commons’ culture, media and sport committee, and to provide further details on the Panorama episode in his response to the Commons culture media and sport committee, which had asked how he would address the concerns.

Speaking after the resignations, the government minister Louise Sandher-Jones rejected suggestions the BBC was institutionally biased. The veterans minister told Sky News: “When you look at the huge range of domestic issues, local issues, international issues, that it has to cover, I think its output is very trusted. When I speak to people who’ve got very strongly held views on those, they’re still using the BBC for a lot of their information, it’s forming their views on this.”