As someone who has lived in London for over 20 years it still amazes me when I find such great, and often undiscovered open spaces in amongst the contrete jungle.
I had the joy of taking Betsy for several walks on the Leytonstone side of Wanstead Flats recently, which I believe is know as Bushwood, a walk I had yet to discover.
It amazed me how quiet it was, and how vast and open the space was, which is great for throwing balls and frisbees. It has the added bonus of a wooded area where you can escape to on hotter days to cool down.
You can walk for quite some time without meeting anyone, and generally those you do meet are others with dogs, so a nice bit of socialising can be had also! We even met a tractor one day, and you could be forgiven for thinking you were in the countryside and not in the middle of the UK's capital city!
There are several ways to access the area, but I walked down from Hartley Road, E11, if you haven't walked your dog in this area, give it a try, it makes for a pleasant change.