The Westminster Abbey event was due to be hosted by the BBC the Sun newspaper reported, but it quoted a source which claimed the plans were switched to ITV after a row over the programme which examines William and the Duke of Sussex’s relationship with the media.
Kate is reportedly hosting the programme and there is speculation that the couple’s children, Prince George, Princess Charlotte and Prince Louis, may feature in the show.
The BBC has been criticised by the royal households for giving credibility to “overblown and unfounded claims” in the documentary.
The first episode of The Princes And The Press, presented by Amol Rajan, aired early this week and included suggestions that negative stories about the Duchess of Sussex were leaked by courtiers and there was a competitiveness between households.
The second episode, due to be screened next week, is expected to delve into William and Harry’s rift, and royal aides are reported to be concerned it will include claims the brothers briefed against each other in the press through their advisers.
Richard Sharp, chairman of the BBC, has said that occasionally programmes from the broadcaster “may not meet with full agreement” with establishments, including the royal family.
Mr Sharp was asked at the VLV Autumn Conference about reports that Kensington Palace had elected to switch the screening of its Christmas Carol service to ITV following a BBC documentary about the royal family.
“The BBC is a national institution and we approach our relationships with the other national institutions with great care and thought,” he said.
“The royal family is at the centre of our identity, it’s underlying importance is unequivocal.
“We have tremendous respect for all aspects of the royal family in that they undertake and do.
“From time to time this organisation produces programmes which may or may not meet with full agreement with different parts of the establishment.”
“Our job is to get that right, to be independent, to be respectful.”
The Sun reported a source as saying about the Cambridges’ Christmas show: “It was all arranged to be on BBC1 but it was switched in the last few days because of the terrible row over the documentary.”
Buckingham Palace, Clarence House and Kensington Palace took the rare step of issuing a joint statement to the broadcaster which was included at the end of the BBC Two documentary.
The statement from the palaces 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.”
Kensington Palace and the BBC declined to comment and ITV have been contacted for a comment.