A more fun way to find travel partners and not pay tour fees would be to join a social networking group. There is one that I was in, in Washington, D.C., that was great (and free), and it has a London chapter (the London chapter isn't nearly as huge as the one in D.C., but it's worth a look).
It's called Meet In, and the web site is
http://www.meetin.org/. On the left side of the page are lists of cities; scroll down until you find Europe, and you'll see London. Just click!
FYI, this isn't a dating site -- it's networking, finding friends to hang out with and do stuff with. Most of the stuff will be located in the town you're at -- people host events, and you just sign up online (no fee) and go. This would be like going to a museum, or a movie, or a pub night, or whatever. This is a non-profit group started by a guy who just wanted to hook up and make friends, and there's no cost whatsover. If you go to a movie, you buy your own ticket, of course, but there's no fee to be a part of meet in.
They sometimes do trips, too. And there are meetin groups everywhere, so say you want to go to Paris. You could organize a trip with other London Meetin folks, or you could just strike up a friendship online with some Paris folks and hook up with them and go to their events while in Paris. Easy and fun! When in D.C., I had planned a trip with Meet In folks from around the world to go to London and Paris -- but then knee problems hit hard and I had to cancel my end. Everyone else went though, and there were people from all over. I couldn't speak highly enough of my experiences with the D.C. meet in group as a way to make friends to go explore your city or other cities with.