More than 150 Royal Navy, Royal Air Force and British Army veterans wrote to the Queen, calling on her to strip Prince Andrew of his ranks and titles in the armed forces.
The 95-year-old head of state is commander-in-chief of the army, navy and air force.
"Were this any other senior military officer it is inconceivable that he would still be in post," they wrote in a joint letter made public by the anti-monarchy pressure group Republic.
"Officers of the British armed forces must adhere to the very highest standards of probity, honesty and honourable conduct.
"These are standards which Prince Andrew has fallen well short of," they said, adding that he had "brought the services he is associated with into disrepute".
Senior members of the British royal family have typically been appointed as honorary heads of military units, with the Queen´s approval.
Andrew was honorary colonel of the Grenadier Guards, whose soldiers guard Buckingham Palace in their distinctive bearskin hats and red tunics.
Royal patronages are associations with charities and other organisations.
Andrew, a former Royal Navy helicopter pilot who flew in the 1982 Falklands War, is accused of sexually assaulting Virginia Giuffre when she was 17.
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