Channel 4 will broadcast photos of the crash that killed Princess Diana despite a plea from her sons.
The princes' secretary said they felt compelled to speak out
Prince William and Prince Harry's private secretary wrote to the channel saying they felt it would be a "gross disrespect" to their mother's memory.
Channel 4 said it decided to run the images in the documentary on Wednesday after considering the princes' concerns against wider public interest.
The pictures by French photographers are of the August 1997 crash in Paris.
Diana, 36, Dodi Al Fayed, 42, and driver Henri Paul were killed when their Mercedes crashed in the Pont de l'Alma tunnel in Paris as they drove away from paparazzi after leaving the Ritz Hotel.
The letter from the princes' private secretary, Jamie Lowther-Pinkerton, was sent to Hamish Mykura, head of history, science and religion at Channel 4, last Friday.
Mr Lowther-Pinkerton wrote: "If it were your or my mother dying in that tunnel, would we want the scene broadcast to the nation? Indeed, would the nation so want it?"
In particular, the letter asked Channel 4 to remove several images of the crashed car with Diana still inside and of a medic treating her which appear in the documentary called Diana: The Witnesses In The Tunnel.
"These photographs, regardless of the fact that they do not actually show the princess's features, are redolent with the atmosphere and tragedy of the closing moments of her life," Mr Lowther-Pinkerton added.
The BBC's royal correspondent, Nicholas Witchell, said he believed the letter was instigated by Prince William.
He said the second-in-line to the throne was taking a stand and making sure his and Harry's objections were known.
In an interview with the BBC on Tuesday Mr Lowther-Pinkerton said it did not take "any imagination" to realise why Prince William and Prince Harry would be offended by the programme.
Conservative leader David Cameron said the broadcaster needed to ask itself: "Are we making this programme because there's a genuine public interest, or are we just being prurient?"
He added: "If the latter answer is the case, they shouldn't do it."
Lib Dem Shadow Culture, Media and Sport Secretary Don Foster backed Channel 4.
"Channel 4 is right to refuse the princes' request to change the programme," he said.
"While any programme about Diana's death will cause distress to some members of the Royal Family, there is a legitimate public interest in the event, especially from a programme which provides new insights.
"Most commentators who have actually seen the programme praise it for the sensitive way it deals with a very delicate issue."
Lord St John of Fawsley, who was a friend of the princess, has demanded an inquiry into the screening of the images.
'Distress not intended'
He said: "This is worse than tabloid journalism, because everybody knows when they pick up a tabloid what to expect.
"But when you see a serious programme meant to be dedicated to the arts and intellectual matters and history, really going down into the gutter in this way, this is something which must be condemned."
Head of Channel 4 Julian Bellamy said it had not intended to cause William and Harry distress and did not believe its decision was disrespectful to the memory of the princess.
He said the programme went no further visually, or in tone, than many previous British TV and newspaper reports.
"We have weighed the princes' concerns against the legitimate public interest we believe there is in the subject of this documentary and in the still photography it includes," he said.
He added that photos and interviews provided the "most detailed and credible eyewitness account yet delivered" of the crash.
And Channel 4's Hamish Mykura, who commissioned the programme, said the film was not disrespectful to the memory of the princess.
"What we don't do is cross the line of showing the dead or the injured," he said.
Clarence House said William and Harry felt they had no choice but to make their feelings public.