Rishi Sunak is facing calls to make the process of appointing Richard Sharp’s successor as BBC chairman more transparent.

Mr Sharp’s decision to stand down came after Adam Heppinstall KC’s review found the former Tory donor twice breached the code governing public appointments, risking the perception he was not independent from the then-prime minister.

The Prime Minister faced calls from Labour and the Liberal Democrats for changes to how the BBC chair is appointed as the long-awaited report renewed scrutiny on the current process.

Labour called for a “truly independent and robust process” to find a new BBC chair as shadow culture secretary Lucy Powell said the row had damaged public trust in the broadcaster.

Speaking at Media City in Salford, she said: “That breach and that failure, that this report found today, has done untold damage to the reputation of the BBC.

“That’s why these processes exist, because the whole point is you have to declare any conflicts of interest that should they come to light later on would cause reputational damage to the BBC.

“That’s exactly what’s happened in this case.

“It is not a minor indiscretion. It is a clear failure of the rules. He breached the code.

“He should have declared he had this murky, cosy financial relationship with the then prime minister, who then appointed him only a matter of weeks later.”

Liberal Democrat leader Sir Ed Davey added his voice to calls for a “rigorous, transparent and independent process to appoint the next BBC chair”, as he argued for a “confirmation vote by Parliament’s cross-party Culture, Media and Sport Committee”.

Damian Green, acting chair of the Culture, Media and Sport Committee, said the person who replaces Mr Sharp must have “the integrity and impartiality needed for this role”.

The senior Tory MP said: “The undoubted damage Mr Sharp’s failure to disclose perceived conflicts of interest has caused to trust in the BBC, the public appointments process and to Mr Sharp’s reputation could all have been avoided had he chosen to be more open with the facts when he appeared before the committee more than two years ago.

“Mr Sharp’s resignation shows that pre-appointment hearings should not be seen by candidates as a minor inconvenient hurdle to be brushed aside, but as an important part of a process to ensure the right person is appointed to the job.

“We hope that lessons have been learnt by all those involved so that future appointments are not clouded in the same way and people can have faith in those chosen for public positions.”

John Nicolson, the SNP’s culture spokesperson, tweeted: “Richard Sharp is right to resign. He should have resigned weeks ago instead of leaving the BBC rudderless and the staff in limbo. His replacement should not be a Tory Party donor.

“Labour must now promise that it will not reward party donors with plum public service jobs.”