The details of the letter come a day after the corporation’s chair, Samir Shah, told a select committee of MPs that he believed he had consulted Banerji, and the pair had had a “26 minute call”.
Banerji told BBC News on Tuesday he had followed the discussion at the committee with interest.
He added: “My resignation letter might clarify my reasons for resigning. It might also serve to inform misconceptions which may have arisen for committee members and viewers.”
​​Davie and Turness resigned as a result of the fallout over a Panorama episode that edited together parts of a 2021 speech by US President Donald Trump.
​​It was sparked by a leaked memo to the board sent by a former external adviser, Michael Prescott.
​​Since then, concerns have been raised in some quarters about how the BBC board operates. The board is responsible for oversight and strategy of the corporation.
​​In his letter, Banerji wrote: “I will not be seen as a participant in a board decision on which I was not consulted, nor one which in my view has had adequate discussion.”
​​On Monday, Shah was asked directly by MPs about Banerji’s resignation and rejected his claims that he hadn’t been consulted about the events leading to the departures of Turness and Davie.
​​”I am both disappointed and surprised by what he has to say”, Shah replied, telling the committee: “I would say he was consulted”.