On the day of Anne Boleyn's execution, Henry VIII obtained a dispensation for him to marry Jane Seymour, although in the third degree of affinity. To my understanding, he meant her second cousin.
Now Jane and Henry were only fifth cousins, so I assume he had an affair with her second cousin. I can't find out who this might mean! I know she was related to the Bryans, so thought it might mean Elizabeth Carew (nee Bryan), the wife of Nicholas Carew and the sister of Francis Bryan. But I can find no mention of how closely related they were.