We were scheduled in at the Museum of Docklands to meet some pirates, and see if they wanted to recruit a new, slightly too small, deckboy. Kit seemed to suit the pirate lifestyle.
It was a great exhibition and really little person friendly. There was even a spot on the boat to sit and have a story (kid's books provided), although the light was slightly bad in there (as the pics show), and my little pirate didn't have time to sit down for a story because he had treasure to find.
More generally the Museum of London, Docklands is a great place to take a toddler. There is a great free soft play area and they always have family activities for all ages. Plus you get to ride on the DLR to get there, which is exciting enough on it own!! :)