Did a quick little experiment now to test that, though - both on the Guardian and the BBC websites, the overwhelming majority (as in, by a factor of ten or more) of hits has "medieval". One of the hits for "mediaeval" on the Guardian's site is their style guide - mentioning that one should write "medieval", not "mediaeval".

So I think it's really an archaic minority spelling even in Britain, which would also explain why I'm not used to seeing that spelling at all even though the majority of my reading is British English rather than American.