Why did Henry Tudor invade wales and England?

Blame his mother Margaret Beaufort. Richard III was King at the time, as he inherited after his brother, Edward V, died. Edward had two sons who were to young, so Richard took the crown and sent his nephews to the tower - where they died. Meanwhile, England hated Richard, who was of the Plantagenet blood line and from York, and Henry VII, of the Tudor line and from Lancashire, was in exile in France. Margaret, meanwhile, organised the whole campaign and summoned her son back in time to kill Richard III and take the crown for himself.