As far as I can tell, the main "political" groupings in the C of E are as follows:
- Reform, who believe that no-one else believes the Bible and that it's more important to be right than to be loving
- New Wine, who believe that no-one else has the Holy Spirit
- Forward in Faith, who believe that women smell bad and that making fun of coloured bishops is a good thing
- Affirming Catholicism, who believe that the most important thing is getting your clothes just right
- Sea of Faith, who believe that it's important to believe that it doesn't matter what you believe
- The Prayer Book Society, who believe that if we change anything from the way it was in 1662, we're dooooomed.
- Fulcrum, who believe that it's important to be nasty to anyone involved with Reform, whatever they do
All the above descriptions are of course parodies, but all have at least an element of truth. And that's why I'm not into church politics.