According to Battle of Brothers by royal biographer Robert Lacey, the siblings fell out when Prince Harry was pictured in a Nazi costume at Maud's Cotswold Costumes in January 2005.
While Prince William chose an animal costume, Harry, who was 20 years old at the time, wore a replica Nazi uniform. The khaki-coloured outfit had collar flashes, an eagle insignia on the chest and a red, white and black swastika armband.
Prince Harry released a statement at the time saying he was “very sorry if I caused offence or embarrassment to anyone”.
The incident sparked national uproar as photographs of Prince Harry in the costume emerged in the press.
In the book, Lacey alleges that the ordeal left Prince Harry feeling alienated from the royal family.
“For the first time, their relationship really suffered and they barely spoke,” the book states.
"Harry resented the fact that William got away so lightly."
Lacey also claims that Prince’s nanny, Barbara Barnes, taught them to walk, talk and read while their mother, the late Princess Diana, was preoccupied with humanitarian commitments and health concerns.
Barnes was ultimately dismissed, Lacey claims, and was not allowed to say goodbye to the Princes.
Lacey writes: "Following the death of Diana in 1997, people remarked on how well the two young princes reacted to the unjust and unexpected removal of a mother figure from their lives - surprised, bewildered and distraught though they were.
"In fact, ten years earlier, they'd had a little practice."
The book also touches on the departure of Prince Harry and Meghan Markle from the royal family, with Lacey claiming that the Queen thought the couple had been “erratic and impulsive”.
Meanwhile, Harry and Meghan’s trademarking of “sussex royal” prior to their departure was allegedly widely frowned upon within the royal family, who Lacey writes were “hopping mad” over what he terms this “commercialising of the crown".
Battle of Brothers is currently being serialised in the Daily Mail.
The Independent has contacted representatives for both Prince William and Prince Harry for further comment.
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