P1976, I don't think this comes down to wanting to 'change' things in the sense of reversing the Mayor's decisions, etc. That's just a non-starter, really.
But if you win as an independent councillor it does mean having a legitimate platform to give voice to what matters to Forest Hill residents and business people - and making it publicly uncomfortable for our local councillors to nod through whatever their Labour lords and masters want. The press will love you.
Besides - there are things that councillors do to help their constituents that don't need a council vote. One of my councillors sorted out a long-standing problem of a missing weight-restriction sign on our road - a problem that 'Fix my street' never managed to resolve but which our councillor sorted within a couple of weeks.
As for a pressure group, there's already the Forest Hill Society, which does sterling work. Maybe they could do with an extra volunteer, or maybe it's a way of learning more about some of the workings of the local political machinery and getting some experience that will serve you well in your 'manifesto'.
Just do give some thought to the high profile nature of being a councillor, especially one as outspoken as you like to be. As I said, the press will love you for being outspoken when you're up against the mighty local Labour party - but the press is always looking for something to blow out of all proportion, too.