On my way to Zambia in June, I have a stop in London for a partial day. I'll be there from about 7am to 4pm (flight leaves around 7pm). I've never been to London before, and would like to see as many sights as possible in the short time I have. My interests are primarily historical places, but am certainly open to anything that's interesting.

Currently, unless I get a better suggestion, I'm planning on taking the tube or subway or whatever it's called from Heathrow into town and back.

Right now, my inclination is to do as much of this walk as possible. I'm most interested in getting feedback on what's actually worth paying to see and what's better just to look around outside and move on.

Also, there's no indication as to the distances and time involved in doing this walk. Or, should I ditch this area and see something else altogether?