Lady Margaret Beaufort ( May 31 , 1443 â `` June 29 , 1509 ) of the House of Lancaster was the mother of King Henry VII of England and grandmother of Henry VIII . Lady Margaret Beaufort ( 31 May 1443 â `` 29 June 1509 ) , later Countess of Richmond and Derby , was the mother of King Henry VII and grandmother of King Henry VIII of England .