I'm almost completely certain there has neither been a Green HoS nor a HoG.
The Green candidate in Finland's last presidential election ended as runner up with 37% of the vote, but that's the closest anyone has come so far... well unless you count Prince Charles, he's technically been a heartbeat away from it for years, but it's not like Old Liz intend to die anytime soon.
I have always wondered about the Royal Families private political views. What proof is there that Charlie likes the Greens though?