Wouldn't English m-a-arms own North European armour?

A Late Medieval era English man-at-arms should be able to afford very good armour (+ several horses, a well armoured squire, vallet, an archer or two.). Apparently, English men-at-arms were there during the defense of Constantinople during the 1394-1402 siege. It is an interesting question (the answer to which I don't know) about possible English involvement. The best armour Constantinople had access to was Italian obviously. So they were armoured as well as the Empire could.

They were supposed to be an elite guard unit. So, by this time they weren't really Scandinavian. One question though : shouldnt the varangians have more norse looking or english looking armor ? The current one seems to have a more Italian influence.The Varangians are a late era unit.