Police said they are also getting in touch with Lord Justice Scott Baker, the judge who presided over the inquest into her death.
Princess Diana, 36, Mohamed Al-Fayed’s son Dodi, 42, and driver Henri Paul, 41, all died in a crash in Paris in August 1997.
Police are currently carrying out a “scoping exercise” as they look into claims that the trio were murdered by a member of the British Military.
They have not launched a full investigation.
Royal bodyguards and MPs have brushed off accusations that the Princess of Wales’ death 16 years ago was carried out by British special forces who then “covered it up”.
The sensational allegation surfaced in the second court martial of Sergeant Danny Nightingale, the SAS sniper convicted of illegally stashing a pistol and 338 bullets in his bedroom.
The claim was contained in a letter from the parents-in-law of Soldier N, Sgt Danny Nightingale’s former housemate, which was sent to the SAS’s commanding officer in September 2011.
Scotland Yard confirmed in a brief statement this morning that they will be contacting members of the Royal family to inform them about the new developments.
“We are in the process of notifying Princess Diana’s family, the family of Dodi Al Fayed and Lord Justice Scott Baker,” a spokesman said.
Scotland Yard routinely contact relevant parties to keep them informed about what is going on when there are new developments in a historic case.
The eight-page correspondence claims Soldier N boasted it was the SAS that had “arranged Princess Diana’s death” and that it had been “covered up”.
Sergeant Danny Nightingale, 38, was found guilty last month of illegally possessing a pistol and ammunition at a Hereford house he shared with Soldier N.
Soldier N, who is serving a custodial sentence for possessing firearms at the same address, was originally reported to the police by his wife, from whom he is now separated.
The letter was sent to Soldier N’s commanding officer in September 2011 and passed to the Service Prosecuting Authority before the start of the Nightingale trial.
All references to the SAS were removed by the SPA.
The paragraph referring to the death of Princess Diana says: “He also told her [his wife] that it was the *** who arranged Princess Diana’s death and that has been covered up.”
The letter says Soldier N told his wife there is a “box which members of his unit use for private jobs”.
“They put in the box the name, address and details of what they want done and then one of them who wants to earn extra money does that job.”
When Soldier N was challenged by his mother-in-law, he is accused of saying: “Let me stop you right there – I kill women and I kill children.”
As well as hiding weapons in his house, in a “reign of terror” on his family Soldier N allegedly attacked his son after mistaking him for the Taliban.
His children were also allegedly driven around in the boot of his Land Rover and he had hung his son 30ft above the ground in a tree.
An inquest in 2008 found that Princess Diana and Dodi Al-Fayed were unlawfully killed due to the ‘gross negligence’ of driver Henri Paul, a security manager at the Paris Ritz Hotel, who had been drinking.
Henri Paul’s mother Gisele said she believed her son was murdered together with Princess Diana and Mohamed Al-Fayed when the Mercedes he was driving crashed in an underpass.
Gisele Paul, 83, said: “We believe there was a plot to kill the Princess that terrible night in August 1997.
“We know in our hearts that our son was murdered and we still live with the hope that one day the truth will be known.”
The new information was also welcomed by Mohamed Al-Fayed, who also insists the couple were murdered. He said he trusted the Metropolitan Police would investigate the new claims “with vigor”.
A Royal spokesman said there would be no comment from Prince William, Prince Harry or Clarence House.
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