“Every reasonable line of enquiry was objectively pursued in order to fully evaluate any potential evidence. The final conclusion is that whilst there is a possibility the alleged comments in relation to the SAS' involvement in the deaths may have been made, there is no credible evidence to support a theory that such claims had any basis in fact,” the statement said.
“Therefore the MPS are satisfied there is no evidential basis upon which to open any criminal investigation or to refer the matter back to HM Coroner,” it concluded.
A 2008 inquest had found the couple had been unlawfully killed as the crash in the de l'Alma tunnel occurred partly due to the “gross negligence” of the driver.
Egyptian tycoon Mohamed Al Fayed, Dodi's father, was “disappointed but not discouraged” by the outcome, his solicitor Simon McKay said.
He called the scoping exercise “the latest whitewash in a 16-year cover up”.
Princess Diana, the former wife of the Prince of Wales and the mother of princes William and Harry, was 36 when she died in the crash with Al Fayed, 42.