London for free includes the many parks and public spaces that fill the city. Trafalgar Square is free to visit, though you might want to buy some corn to feed the gazillion pigeons that hang out there. London's parks are beautiful places and it is easy to wander through one on your way from one great London attraction to another. Among my favorite London parks-
Saint James Park
Many of London's world class museums are free and are a great place to get out of the weather. My favorite of London's free museums is The British Museum, famous for it's mummys and seemingly unlimited catalog of amazing items. Other great free London museums include
Imperial War Museum
Natural History Museum
You can see Big Ben, Tower Bridge, and St Paul's Cathedral for free. Most tour books have excellent walking tours which will lead you by a lot of the famous London attractions. For me just being in London was a fairly exciting event, so wandering around aimlessly and taking photos of everything in site was a good, free activity for me. It is better to have a plan of action though and map out a few of the must sees before you spent too much time just walking. There is a lot to see and do in London, and it's a good idea to think about what you want to do.
A few websites to find more London For Free Stuff-
London for Free-a nice site that is well laid out and has a wealth of information on all things free in London. Walks, Outdoor Activities, Indoor Activities and London Day Trips.
London4Free-a lot of interesting information on the many free things to do in London. Also covers such things as cheap places to stay in London, cheap things to eat in London, and cheap travel to London and around London.
Free London-From Time Out London. Lots on info on free things to do and discount things to do in London. A fun site to wander around and see what's on.