The Spanish only started using the fleur-de-lys after the War of Spanish Succession, from the 18th century onwards. This happens because, with the death of Charles II and the disappearance of the Spanish Habsburgs, Louis XIV installed a member of his Bourbon dynasty (represented by the fleur-de-lys), his grandson Philippe as King of Spain.
The British only used the fleur-de-lys because they claimed the French throne. That symbol was undisputedly associated with France.