The UI for the English Knight does not seem to be upgraded with either Network of Castles or Network of Citadels, even though it does seem to be affected. It remains at 1.5 no matter what.
This is different than the Man at Arms, which does not show an additional improvement from Network of Citadels. In this case, the MAA does not get affected because of the convoluted way how the attack speed increase is calculated.