The POD is that Henry IV decides to argue his claim on the English crown arguing he was the "heir male" to Richard II. Which Henry IV was unquestionable so. Also he establishes rules for the English royal succession which would be the following;
Firstly, forbidding a female from inheriting the crown and secondly, the crown passing through a female. Essentially similar to what the Kingdom of France had.
Personally I can see Henry VI including his Beaufort cousins in the line of succession. That could make things quite interesting.