Well, the cheapest places in Europe tend to be the ones who haven't converted yet to the euro (that would be most of Eastern Europe). But it looks like you're staying in Western Europe, so I can tell you that I think England and France are generally pretty expensive. Switzerland is very expensive too, from what I hear. I haven't been there yet, so I can't really tell you anything about that beyond what I've heard from others. I was just in Italy a month ago and I thought it was fairly reasonable. Just do research before you go to find out where not to eat and sleep...generally, the closer you eat and sleep to the really touristy parts of town, the more expensive it's going to be. That's a good rule of thumb anywhere you travel in Europe, really. I live in Germany and I don't find it to be too terribly expensive here, although we're getting paid in USD while we're spending in euros, so with the conversion rate, it seems more expensive than it should be. But in comparison to most of the other places I've visited in Europe, Germany is pretty inexpensive.
You're lucky you have free lodging in London though. London is one of the most expensive cities in the world. Outside of London, it will be considerably less expensive.
If you want to get more info, you can always leave me a private message. I would be glad to share with you what I know. I also have some ideas for inexpensive hotel chains, if you're not picky about where you stay and want clean, basic lodgings.