If you check some of the London guides, they will tell you which numbered bus to take to see a lot of the sites for free. Buy an all day pass for bus/subway and you can ride to your heart's content - and the joy of London is that everyone speaks English so even if you end up someplace where you're not sure how to get home, just about anyone can help you with directions. If you see something you want to look at closer, just hop off and when you're finished your self tour hop on the next bus going your way.

Pat