Henry Tudor's claim to the English throne was tenuous to say the least, but when he defeated Richard III at the Battle of Bosworth fields nobody was going to gainsay him, least of all Richard who had died in the battle.
When he married Elizabeth of York, uniting the Yorkist and Lancastrian houses, the war of the roses was effectively over. The people were so greatful to Elizabeth that they styled the image of the queen in the deck of cards after her. This is why to this day the average deck of cards carry four Tudor women.
Henry VII decided to strengthen his dynasty's grip on the throne by naming his eldest son Arthur. Arthur died before his father, so his younger brother Henry inherited both Arthur's throne and his wife.
Despite the fact that the Tudors were Welsh, he still persecuted Welsh for not speaking English.
In the 'Henry' line came after the 6th one, but before the 8th.