Read the history of the Spencer family that I linked above. Winston Churchill is a related member of the Spencer clan as well.
Also @Denville's reference to Fergie being from 'landed gentry.' So what? So is Camilla from the 'landed gentry' class, which is below the aristocracy/nobility.
And yes, the Spencers are aristocrats who are related to royalty via illegitimate ancestors:
"Today's Spencers are direct descendants, albeit illegitimate, of the House of Stuart, with the family boasting at least five lines of direct descent from the Stuarts; and from them, the Spencers can trace their ancestry to other royal houses such as the Bourbons, the Medicis, the Wittelsbachs, the Hanovers, the Sforzas, the Habsburgs, and the Houses of Howard and Boleyn through Mary Boleyn, Mistress of Henry VIII of England."
Also the term 'commoner' in the U.K. refers to "a person who is not born into a position of high social rank."
That absolutely does not describe Diana or her family! She was not born of royalty, but she was a member of the aristocracy/nobility. The ancestors who began as sheep farmers is not recent. It's very far back. Still, there's nothing wrong with sheep farmers, but Diana did not grow up the daughter of a sheep farmer! Another famous ancestor of Diana's was Lady Georgiana Spencer who married the Duke of Devonshire (another famous British aristocratic family).
Interestingly the Spencers were also related to George Washington's family.