As starter of original thread 5 years ago I am happy to contribute again!! This summer I have done Princess Diana playground which I really heartily recommend as was wonderful and I had ages 14 right down to 5 with me! I hear there is a nice beach at the South Bank this year too.
Queens park in kilburn is wonderful with outdoor pool ( knee height ) and sandpit and play area and animals and all for free although the parking fees will kill you ( £9 for 4 hours!!).
Cassiobury park in watford also great on hot day - showers of water, little train, bouncy castle etc
did museum of londn a few days ago which was great. Really worth the drive - something in there for all primary aged kids although for toddlers not great choice.