The royal households have taken the rare step of issuing a joint statement criticising the BBC for giving credibility to “overblown and unfounded claims” in a documentary aired on Monday night.

The first episode of the two-part The Princes And The Press programme, presented by Amol Rajan, explored the relationship of the Duke of Cambridge and the Duke of Sussex with the media, including suggestions of royal sources briefing journalists behind the scenes.

In a statement given to the BBC, and shown at the end of the programme, Buckingham Palace, Clarence House and Kensington Palace said: “A free, responsible and open press is of vital importance to a healthy democracy.

“However, too often it is overblown and unfounded claims from unnamed sources that are presented as facts and it is disappointing when anyone, including the BBC, gives them credibility.”

During the programme, a lawyer for the Duchess of Sussex also responded to reports in 2018 about Meghan’s alleged treatment of palace staff.

In March, The Times newspaper reported that the duchess allegedly drove out two personal assistants and “humiliated” staff on several occasions, which she denies.

An investigation has since been launched by Buckingham Palace and the royal household has tasked an external legal team to assist its human resources team looking at allegations made against the former Suits star.

Jenny Afia, from the law firm Schillings, told Rajan on the programme: “Those stories were false. This narrative that no one can work for the Duchess of Sussex, she was too difficult and demanding as a boss and everyone had to leave, it’s just not true.”

Following the airing of the programme, a report published in The Sun claimed that William banned aides from briefing against family members.

According to the newspaper, the duke was “clear” he did not want aides to say anything about the other households after he saw reports during the split of his parents.