I think all Islington primaries are fine, pretty sure they are all at least Ofsted good. I don't know about Camden.
from a teaching point of view schools have become very focused on levels and data rather than actual classroom experience
It seems to me that the schools where they can afford to let it all hang out, not do homework and generally have a less regimented (and sometimes no-uniform) approach are predominantly the very MC ones with not many children on free school meals/arriving with low achievement levels/ESL etc. If that is what you are looking for then move next door to Yerbury, Eleanor Palmer, St John's Highbury etc - Ofsted has already rated these schools outstanding and most likely won't come bothering them too often.
Schools where they are very concerned with levels, data etc are generally the ones where they really need to measure children's attainment and check that all children are making progress, including those who started at a low level. So I think it's a bit unfair to criticise them for doing that! FYI my DC is at a lovely Islington school. Not one of the well-heeled ones and the MC children are very much in a minority - but they thrive there and achieve well academically, and are learning to get on with all kinds of other children, not just those from similar backgrounds.
I guess by good I mean I want a school where the schools main priority is the children and the communication and involvement for parents is good.
I think all schools that are even half way good would say that their main priority is the children!
As for parental involvement, in my experience that is very much a MC thing. It can be ruthless though - woe betide you at Yerbury if your cupcakes aren't up to scratch! And if the parental involvement isn't great where your DC end up - you can always get involved yourself. A school that doesn't have an active PTA will be super grateful for your help in setting one up.
Good luck, wherever you end up.