If there are still tix, look out for Polka theatre's THE GRUFFALO'S CHILD, also, for younger ones, I really do recommend BEAR STORIES (alos Polka) for either 1-2 years or 3-4 - it's on until 5th Aug.
We will be at Brockwell Lido, Brockwell Park paddling pool, expoloring nearby places we don't usually get to like SYDENHAM WOODS (great for running through and a shady picnic, and you might see the urban-mythological Sydenham Panther which is reputed to live there).
Don't forget the dinosaurs at Crystal Palace Park - also the maze. They have a junior park rangers club of some sort that you can sign your child up to - it operates all year, with weekend events, but has special days in the summer.
We like to get a rowing boat on Battersea Prk lake once in a while, then run through the fountains.
The Livesey Museum, which has an inter-active MYTHS AND LEGENDS exhibition
Vauxhall City farm
Surrey Quays City Farm (is it called that?)
Kew is good for an all-day outing - expensive for adults - £11, but they don't charge for children, there is the excellent play area, ds loves the badger sett, and spotting things we eat, like avocados, in the tropical houses, and the bubbling mud in the evolution house. If you take your own food it's not a bad value day out.
Did you know that you can join a real carnival camp in the run up to carnival? You can go every day (or every so often) to help make costumes, and by buying a costume, you can take part in carnival - either on children's day or the adults day. A long day of dancing, but it's the only way to really enjoy the day at Notting Hill (if you must go), imo! Children who can help with gluing and sticking will be welcomed, too. Find your nearest carnival mas camp here
I also like Bushey park (train to Hampton Wick for the Hampton Wick gate - also potter by the river) to see the deer and picnic).
Easy seaside destinations by train: Whitstable or a bit further along, Swaleclliffe.
And trips out if driving - we liked Battle - great inter-active tour of the battlefield and Abbey - and Arundel castle.