It is worth looking carefully at whoever is running any school. For example a decade or two back Wandsworth Council's education department had a far better reputation than Lambeth's and their schools were correspondingly sought after. (Actually quite a model for economic generation as 30 years ago both boroughs were in a similar place economically but good schools helped bring in a more affluent working population including entrepreneurs, and an impressive virtuous circle was introduced.)
I am not sure I would worry too much about, say, venture capitalists. I was told at one point by someone who should know, that an additional 1,200 children looking for private school places are coming into London each year. This has resulted in a hefty expansion of prep school places (Fulham Prep, Knightsbridge Prep, Newton Prep and many more are less than two decades old and many existing schools have grown) leading to an 11+ log jam, especially for West London boys. The advantage of backing from venture capitalists is that they can raise the money for a big bang. First rate facilities from the get-go, a head-hunted Head, experienced Heads of Department recruited first. Build the reputaiton, wait five or so years and then put up the fees and reap the profits as parents clamour to get their children in. Each will have its own USP but they will only survive if they deliver what the customer wants.
My guess is that the need to balance the books early and thus recruit inexperienced teachers has led to instability in schools like the West London Free School. I would be particuarly interested in knowing who was behind any Free School I was considering and how much start up capital they had to get the school running.
One reason we ended up taking the private route was our state alternatives were not at all attractive. At the time the local secordary had 93% on free school dinners, and indeed when my son got to 11, our LEA was unable to offer him any place at all. Apparently at the time they were short 20 Primaries and 3 Secondaries. In fairness the local school has improved immensly, but is still seen as focussing on providing a safe learning environment for those from more challenging backgrounds rather than stretching the more able. Hence local disappointment when people heard the newly announced Free School will be run by an evangelical Christian group. It did not take too much Googling to find links between some within the Church and the creationist movement.
London's population growth means more schools are needed, both state and private. Governments (this and the last) have clearly decided that they cannot afford the capital funding and so have looked to other sources. This means it is more important than ever to know who controls policy at your child's school and what their motives are. I get venture capitalists and profit. I would be very wary of a non-mainstream religious group.