Under English law, any child born to a Royal out of wedlock is ineligible to succeed the throne, which extends to the child's heirs. This can never be reversed, even if the child is legitimated by the Royal parent. Therefore, despite being the "only" surviving member of the Windham line, Ralph could never take the throne since his father was born out of wedlock.
While this movie is fictional, King Ralph and King Cedric would not be titled as Ralph I and Cedric I. They are only numbered as such once there has been a second monarch of the same name. Hence Queen Victoria is not referred to as "Victoria I."