My advice is to try and visit as many of the free attractions as you can, such as Tate Modern, Science Museum, Changing the Guard and Westminster Abbey. There's lots of things happening all year round in London's South bank; free events, exhibitions, debates and festivals. Try this website -
London is Free - Your online guide to free events in London.
If you're set on visiting the attractions with admission fees then work out if it's worth investing in a London Pass. These aren't cheap but if you cram as many of the 50 free attractions in as you can, you should save money.
Also, if you collect tesco clubcard points, these can be exchanged for some great days out such as Kensington Palace, London Zoo, Tower of London and many more.
If you've got any suggestions let others know about them here.
Sammy