The two main branches are indeed German and Italian. However, the position of ARMA (for example) is that there was ONE pan-European longsword tradition, with regional variances. I can certainly see their line of reasoning.
I see their point and share some of their opinions on this but I think the main thesis is too simplistic and needs to be much more nuanced than is currently (usually) presented.
I think that what's more likely is that there were local sword masters which famliarized themselves with the weapon, in practice and in combat, and developed their own, regional, styles in response to the basics of what is required by the blade itself and interactions with other regional styles.
Sort of a mish-mash of general knowledge, regional independence, divergent evolution, and individual creativity/stylization.
Not that I'm anyone to listen to though.
There are verses on English longsword that are being presented by two ARMA members along with interpretations in an upcoming publication.
And some non-ARMA folks, ims.
It's really interesting to see people running with the English Longsword. They've got a long way to go with it but it's a beginning.
From what I've gleaned part of the issue is the paucity of source material. Only three "sources" and, of those, only one that has anything even aproximating "detail" (and that's stretching the word).
Still I'm excited for them and wish them lots of luck.
Peace favor your sword,
Kirk