DBWI Scottish dynasty inherits crown of England

What would have been the effects of one of the Stewarts, for example, inheriting the crown of England?

An obvious POD is the War of the Roses eliminating literally every potential noble with a claim to the thrown. However, one of Henry VII's daughters married the King of Scotland, so a more likely POD would be the Tudors somehow dying out in the sixteenth century.
 
Dying out? Not very likely what with King Arthur having eight surviving children. Hmm - could Margaret Beaufort somehow marry a King of Scotland maybe?
 
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