I backpacked through Europe for a couple of months a few years ago...and having hit most of the countries there I would certainly recommend basing your itinerary on how long you have.
If you've got a week, don't try and hit five countries, because you'll miss 99.9% of what there is to see in every one. If you have a month, you can do a little more.
With short period trips I would recommend picking a region and sticking to it. For example, if you're dead set on London, try just fitting in the British Isles, Belgium, a little bit of Northern France and perhaps some of Western Germany.
If you wanted you could dedicate an entire vacation to Italy.
Also, Portugal, Spain, and Southern France is a great combo.
Just think about what you absolutely want to see. Prioritize the list, and choose the region that is right and that will be coverable in the time period you have alotted to travel.
My number one recommendation before you go, though, would be to invest $30 in a "Lonely Planet: Europe" travel book. It will be your Bible.
Happy planning!