Forget the Eye. Go up the tower at the Garden Museum: adults £4, under 18s free, for a good view of the Westminster side of London. It's right by Lambeth Palace (Archbishop of Canterbury). You don't have to buy entrance to the Museum to go up the tower. If you want to go to the Leake Street tunnel (recommended) you can walk between the two through Archbishop's Park, which has a playground and used to have a zipwire, although I don't know if it still does.
For views of the City side of London go up the Monument. £5.80 adults, £2.90 children. The church of St Magnus the Martyr, between the Monument and the Thames has a nice model of the original London Bridge with all the buildings on it. It's free but closed Saturdays and Mondays, otherwise open 10-3 normally.
Both towers involve lots of steps so you can get some exercise, but they also let you spend as long as you want at the top, so take some kind of map and have a good look at where you are. You can really see how the river bends through London.
A fun lunch can be had by going for Dim Sum in China Town. Some of the restaurants have trolleys that go round and you point to what you want. Others have a card of pictures to choose from. They mark what you have on a card on your table, so you can order a few items at a time, according to how full you are getting. Dim Sum dishes are around £3 each at eg. New Loon Fung, Gerrard Street, but there are many good ones. Bottomless Jasmine tea isn't much (tip the lid in the pot to indicate you need more water added), and goes well with the food. The DCs might enjoy it - it's an unusual taste, but not unpleasant - or you can always order tap water (or the usual drinks - at a price). The Wong Kei is famous for being cheap with service that's abrupt to the point of rudeness, but it's certainly different. It's also fun to explore the Chinese supermarkets in the area and grab a cake at Bake in Wardour Street.