All I know is, with a Millie in charge of the Labour Party, it must be Neil Kinnock's worst nightmare!
Seriously though, I doubt there will be much of a change. Sure, Ed was the Milliband that positioned to the left, but I don't think there was much substantive difference than David, and any meaningful shift to the left inside the Labour Party will probably be on the grassroots level.
"If communism means anything at all, it means the radical eruption of democracy. Bursting its present narrow political confines, where it is allowed to hold truncated and partly illusory sway, democracy is to engulf all spheres of social life."
~Moshe Machover, "Collective Decision-Making and Supervision in a Communist Society"
" I swear the neighbours must have heard the facepalm I just made."
~Majakovskij