After reading about stirrup controversy, I realized that a lot of sources on the internet, as well as the book I'm reading right now (History of England by G.M. Trevelyan) are possibly not up to date to the latest scientific knowledge, so I decided to ask here to clarify it.

Did the success of Norman conquest depend on using cavalry, as opposed to anglo-saxons of the time, who rode on horses, but fought like infantry? This is what the History of England says, but it seems strange that such important technological advancements (stirrups, saddle, the skill of horseback fighting) would spread on one side of the english channel and be absent on the other, especially given the trade between two regions. What should I read about the topic that is up to date and correct?