Former chief superintendent Dai Davies, the Met's head of royal protection when Diana died, said an inquest and two police inquiries had proved her death was "an accident by any definition". He said: "I'm mystified ... how any new information can possibly allege anything other than [that] this was a tragic accident."
The murder claims were made in a seven-page handwritten letter by the parents of the estranged wife of "Soldier N", a former member of the SAS who was a key prosecution witness at Nightingale's trial.
In September 2011 they wrote to the regiment's commanding officer, raising concerns about their son-in-law's allegedly erratic and threatening behaviour.
The letter, which was censored before being released to the court martial, states: "He [Soldier N] also told her [the daughter] that it was the XXX who arranged Princess Diana's death and that has been covered up. So what chance do my daughter and I stand against his threats?"
The woman's parents also wrote of how Soldier N had told their daughter he could make her "disappear" and described his "killing escapades" while with the SAS, Channel 4 News reported. But Wharfe said the source of the claims of SAS involvement in the Princess' death raised questions about their truth.
"If these parents were so concerned that this information was relevant or had some general import, then they should have delivered it to the inquest," he said. "Why has it taken so long to air this new information? It seems so shallow to me."
Military sources dismissed the allegations of SAS involvement in Diana's death in a car crash in a Paris underpass on August 3, 1997. Colonel Tim Collins, a former SAS officer, said: "It's utter nonsense. This is just wishful thinking on the part of somebody."
Another senior officer said the claims were "a pretty wild idea".