Do the BBC describe him simply as being left wing ? Or is it left wing the context of the Labour Party ? Most of us who follow UK politics would know what that means, and his track record as a 'rebel', especially since the rise of 'New Labour', is a part of that.

Is their a similar widely understood and easy to agree on term for David Cameron's position in his Party ? 'Good Soldier Schweik' in the OP seems to indicate that, for him, there is not. Otherwise why the list of possibilites ?