The upmarket underwear brand, which now operates stores in the USA and the Middle East, lost the coveted honour previous year, shortly after its founder June Kenton published her autobiography, Storm in a D Cup, in March.
Since the incident, Ms Kenton explained that it was never her intention to upset anyone.
Her daughter, Jill Kenton, told the Mail: 'I'm so sad for my mum, as she actually wrote the book for her children and grandchildren.
"I never ever thought when I was writing the book that it would upset anyone", Kenton, now in her 80s, told The Telegraph.
Rigby & Peller now trades from nine stores across the United Kingdom, as well as online. "I've had the royal warrant for so long I never imagined that this would happen". One of the most intimate reveals in the memoir is June's description of fitting the half-dressed Queen while the monarch was surrounded by her corgis.
Kenton, who bought Rigby & Peller for £20,000 in 1982 with husband Harold, sold a majority stake in it for £8m.
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"I think it's unbelievable".
Kenton said that the book is mainly about herself - a "gentle" narrative of her life which she is "proud" of and eager to share.
But the BBC understood that Prince Philip was angered by allegations made by owner Mohamed al Fayed accusing the Duke of masterminding the 1997 vehicle crash in Paris that killed Diana, Princess of Wales and his son Dodi.
Other companies that have lost their royal warrant includes Carr's Table Water biscuits, simply because they are in lower demand at the palace, and Harrods, whose owner Mohamed al Fayed allegedly angered Prince Philip with comments about the vehicle crash in 1997 that killed Princess Diana and Dodi al Fayed.
The 82-year-old's autobiography was published in March 2017 and gave details of her royal visits.
"I can confirm the warrant for Rigby & Peller is cancelled but I can't go into the details why", a spokesman for the Royal Warrant Holders Association told AFP.
"However, the company will continue to provide an exemplary and discreet service to its clients".