Battersea Park - playground, crazy golf, zoo, pizza
Morden Hall & Deen City Farm - playground, paddle in stream (spare clothes) cafes at both, garden centre, animals - check farm website for petting times (closed Mondays)
Day trip to Greenwich - riverboat, cutty sark, lunch at nandos, Emirates cable car
Scooter/Skate park at Kimber Rd & playground/tennis/ducks at King George's Park, lunch in Southside (also cinema)
Diana Memorial Park - take picnic, spare clothes, bucket & spade
Southbank - jubilee gardens & walk along river - usually events going on, street entertainers, carousel, watch skate park. Could brave the aquarium if you arrive early enough & can swallow the cost.
Kidzania - I did it in summer with 5yo - would say it's good for that age if they are confident types & you pick the right activities (nothing too complicated). Go for an early slot - book in advance.