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?
Charles: Green
Elizabeth: SDP (pre-continuity)
Philip: Ukip
Harry: Sun reader who doesn't care who runs the country, as long as...
In more seriousness, Wales's public views in this regard include uncontroversial views on sustainability, conservationism, protection of rural England, and his banal dislike of modernist architecture. None of these would rule him out of, or into, any UK political party.