They are: Edward IV, Charles II (buried today in 1685) and William IV, all of whom had a large number of illegitimate children, but none left a legitimate heir.
Edward IV (1442-83) had twelve to fifteen children by various mistresses, including Elizabeth Wydville, but none by Lady Eleanor Talbot, his only legal wife, whose probable remains (CF2 in Norwich) show no signs of pregnancy – thus Richard III was his legitimate heir.
Those ten were purported, until 1483 to be legitimate and not all of the others were recognised during Edward’s lifetime.
Charles II (1630-85) fathered about fourteen children, of whom only James, Duke of Monmouth could possibly have been legitimate. The Duke’s mother, Lucy Walter died before Charles’ marriage to Catherine Braganza, sister of Pedro II, King of Portugal – thus James VII/II was his legitimate heir.
Catherine’s only known pregnancy ended in a miscarriage.
William IV (1765-1837) had ten illegitimate children by the Irish actress Dorothea Bland (“Mrs. Jordan”), whose descendants thrive today, as do Edward IV and Charles II’s lines – thus Victoria was his legal heir.
His marriage to Adelaide of Saxe-Meiningen resulted in five children but three were stillborn, one died after a few hours and the other at three months.