we went yesterday ( sat) and parked right outside the nat hist museum for free - pretty sure it'll be the same tomorrow BUT get there as ear;ly as poss ( 10am opening time) to get the best chance of a space. BTW our 3 yr old loved it there and so did we!
Used to live in Central Croydon where the most bizarre situations could arise - eg you could legally park on a single yellow line in our road on a Bank Holiday, but not in a pay and display box without paying a fee.... Became a sad geek who knew all the local restrictions and would lobby the council frequently (still remember their wonderful temporary one way system where it was possible to drive into my road, but illegal to drive out - by any possible (legal) route!
Needless to say that offstreet parking has become a must-have in my list of things for a home!