Senior officers have also been ordered to find out what action was taken against the soldier who allegedly made the boast.

General Peter Wall, head of the British Army, is said to be furious as the SAS's reputation has been tarnished.

Sources close to General Wall were quoted as saying by the paper that the controversy was "the most embarrassing and potentially damaging event in the regiment's 70-year history".

An officer called it a "fiasco" for a regiment "supposed to operate in the shadows".

The startling allegations over Diana and Dodi's deaths surfaced at last month's courtmartial of Sergeant Danny Nightingale, the SAS sniper convicted of illegally stashing a pistol and ammunition in his bedroom in Hereford.

The claims were contained in a letter from the mother-in-law of Sgt Nightingale's former housemate, a fellow sniper referred to as Soldier N, which was sent to SAS headquarters in September 2011.

The letter was reportedly passed to military prosecutors prior to the start of Nightingale's trial but has only just been brought to the attention of Scotland Yard.