I was just browsing through the Kings of England on Wikipedia and I noticed that there are two King Edwards before Edward I became King of England in 1272.
I looked through the articles but I couldn’t find an answer. I thought it could be perhaps that the first two Edwards were styled as King of the English rather than King of England, or maybe it’s because the first Edwards were Anglo-Saxons whereas Edward I was a Plantagenet?
Those are my best cases, but I thought it was strange they haven’t been counted.
You can see a reply to "If Arthur, Prince of Wales had succeeded his father Henry VII, would he have been King Arthur I or II?" by /u/Valkine at https://www.reddit.com/r/AskHistorians/comments/6po4f3/if_arthur_prince_of_wales_had_succeeded_his/dkrac6v/ .
Mentioning this answer is intended as a starting point, not to discourage more discussion. Further questions, info, and debate are welcome.
Just to add ; in the Cerdicing line, there was an earlier Edward - Edward the Elder, son of Alfred of Wessex and essentially king of a unified England in all but name.