The Princes in the Tower
Neither Richard III nor Henry VII had legitimate claims to the throne of England.
Two young boys had the misfortune to be the heir and the spare to the English throne. They were Edward V, the uncrowned King of England, and Richard, Duke of York. The two brothers were the only surviving sons of Edward IV of England and Elizabeth Woodville at the time of their father’s death in 1483.
When they were 12 and 9 years old, respectively, they were detained in the Tower of London by the man appointed to look after them, their uncle Richard, Duke of Gloucester. This was supposedly in preparation for Edward’s forthcoming coronation as king. However, Richard took the throne for himself and the boys disappeared, their fate never known for certain.
I don’t think there’s much doubt that Richard was the culprit in the boys’ murder. In fact, it’s far beyond a reasonable doubt. On the way to London he arrested Edward’s retinue including the boys’ protectors, their uncle and their half-brother. A couple of months later, they were beheaded. Both princes were subsequently declared illegitimate by an Act of Parliament, in 1484.
Richard seized the crown, as Richard III, and still lives on in infamy. He lost his throne the next year to Henry Tudor at the Battle of Bosworth, the last decisive battle of the Wars of the Roses. So Richard got his comeuppance. Henry VII’s claim to the monarchy was extremely tenuous: It was from a woman (a great-granddaughter of the fourth son of Edward III) and by illegitimate descent. Such ancestry would disqualify anyone not victorious on the battlefield.
The current Duke of Gloucester is named Richard. It’s not clear why the present-day Royals would honor Richard, the usurper and murderer, with a dignified memorial service in a cathedral after his bones were found outside. (Is there nothing that can embarrass them?)