The former Royal butler had come under a preliminary police inquiry after a newspaper reported he had admitted telling "red herrings" at the hearing.

Yesterday the Metropolitan Police Service said in a statement it had reviewed the available evidence and sought the view of the Crown Prosecution Service and (inquest coroner) Lord Justice Scott Baker.

"As a result we have reached the decision that there is insufficient admissible evidence to prove that an offence of perjury has occurred and therefore do not believe it to be appropriate to instigate a police investigation."

After giving evidence to the inquest in January Mr Burrell returned to the United States, where he spends most of his time, but was secretly recorded in a New York hotel admitting that he had not told the "whole truth".

The Sun newspaper reported the former butler's comments, which included the confession: "I was very naughty, and I laid a couple of red herrings."

The coroner subsequently demanded he return to explain the discrepancy but he refused, sending a statement in which he claimed he had simply been drunk and showing off.

Lord Justice Scott Baker, in his summing up to the jury, suggested Mr Burrell's behaviour had been "shabby".

He added: "You heard him in the witness box and, even without what he said subsequently in the hotel room in New York, it was blindingly obvious, wasn't it, that the evidence that he gave in this courtroom was not the truth, the whole truth and nothing but the truth?"

The jury returned verdicts that Diana and her lover, Dodi Fayed, had been unlawfully killed by the paparazzi and driver Henri Paul.

After the hearing ended last month, the coroner made it clear he had no plans to refer Mr Burrell to police. But they received an undisclosed complaint.