You could try taking them swimming if you're feeling brave enough for two. Lots of pools so check out your local borough council's webpages.
I can recommend a boat trip on the thames. Just hop on the ferry with an icecream for a few stops.
There's lots on indoor play centers dotted about too. Not been to this one but the webpage looks fun and you'd only have to pay for the children not yourself.
www.eddiecatz.co.uk/edcatz.html
Also St Catherine's dock is fun to explore. Lots of things to climb on as you walk around (big stones and things). There's the fountain with the dolphin near the hotel which overlooks tower bridge, the children love walking around it and depending on where you sit if the wind blows teh water you can get a light shower which causes much excitement. In the dock itself there are some big bright mosaic's on one of the wall which you can spend ages talking about (giant hand prints, lots of colours and shapes to talk about). Then there's all the boats and make up stories about where they've come from or are going too, and they even have some resident ducks to feed. Also has cafes etc around and you can buy a postcard to send grandma too and 'write' on it as an activity.
It's not very far to walk to the Tower of London from the dock and the children will have just as much chasing pigeons and climbing up and down the steps on the large paved area in front of the tower or along the bit that runs beside the river.
If you walk along the river front a bit on the opposite side heading in the direction of the aquarium, parliment etc there's all sorts of things to keep the children busy. I can't remember exactly where but they have one of those 'fountains' where the water shoots out as jets in the pavement and they had that giant map to walk on down there somewhere too for a while, not sure if it still is there. It is a very long way to walk all the way down there for little ones though, so wouldn't use it as a conecting activity, but can be a half day in itself just wandering along.
If you do head down as far as the aquarium there's a really small park close by (on the green bit in front of the london eye). Lots to see around there too, even if you don't go on the eye or in the aquarium. One of the stalls there had a bubble machine going when we went last which was just as exciting as the ride on the eye itself for my son. He was 6 at the time. There also tends to be street entertainers that way, but obviously can not guarantee who or what will be there when you go. big ben is visible across the river, again all kinds of things to talk about and learn.
Hope you have fun whatever you decide to do!
Gilly