The weather is likely to be bad (cold, raining) some of the time. So I suggest you have several alternative ideas and choose which is best each day. The zoo in the rain is no fun.

The Natural History Museum is a good indoor thing for children, easy to engage with, visually appealing, with a fine selection of cakes in the cafe. Even the most traditionally Victorian part of the NHM, the minerals galleries, can be interesting to children (of all ages): Oooh, Shiny!

The Tower is also good, as long as it's not raining a lot: it's a giant castle with (slightly) scary ravens and old time guards (often sardonic, for the adult entertainment) full of armour and treasure, what is there not to like about that? You have to walk outside between the buildings, hence not good in a downpour.