It has been written on paper with the Kensington Palace logo displayed in blue at the top of the page.

In the letter, Diana thanked a police sergeant for his help in organising a motorbike display for William’s birthday.

Sergeant George Plumb of the Metropolitan Police and the Special Escort Group are believed to have put on the display for the two brothers and their friends on the grounds of Kensington Palace in 1989.

The late princess wrote: “Dear Sgt Plumb, It was so very kind of you and your team to have come here today on William’s birthday – I cannot begin to tell you what pleasure the display gave to all those little people and their mothers!

“I know how particularly busy you all are at the moment, so it meant even more to us that you and the motorbike boys were able to take part in the birthday celebrations!

“This comes with our warmest possible thanks. Yours sincerely Diana, William, Harry.”

The princess, when writing the sergeant is “particularly busy” is believed to have been referring to bus, train and underground strikes staged at the time.

A spokesperson for the auctioneers said: “This letter comes personally signed by Diana Princes of Wales, H.R.H Prince William and H.R.H Prince Harry, dated 21st June 1989.

“It is on Kensington Palace headed paper, addressed to Sgt George Plumb Special Escort Group in Diana’s handwriting.

“It thanks Sgt Plumb and his team who put on a superb display by the Precision Motorbike display team of the special escort group, for Prince William’s 7th Birthday.

“She was particularly grateful to the team for being able to fit this on a day already full of official engagements, which was not helped by the rail, underground and bus strikes, something which strikes a chord today.

“To have an item signed by Diana, William and Harry is quite special.”

The letter was bought from the sergeant by a private collector around six years ago.