Given the amount of evidence that has accrued over the past decade both about Edward IV’s bigamy and the cover-ups, both in his reign and those of the “Tudors”, he can now be classified as having no legitimate and fourteen or fifteen illegitimate children.
Charles II’s record is almost identical, although he was more open about it.
William IV had ten children by a mistress ( Dorothea Bland aka “Mrs. Jordan”) and five by his wife, Adelaide. Of these, four had died by the end of the day they were born, the fifth within three months.
Henry VIII’s case is as complicated as that of his grandfather because all but one of his ten children (Edward VI) were born either to a mistress or a subsequently annulled “marriage”. Indeed, he classified both his surviving marital daughters as illegitimate and there were affinity impediments to his first two ceremonies. The two Careys are not included in these figures but ought to be.