Go-with-the-flow is a great way to go! Just remember, though, that it's the high season, so hostels may be booked up in bigger/more popular cities, so it might be in your best interest to at least set up "waypoint" cities and book at least a night or two for each in advance.
For instance, all the popular hostels in Amsterdam and Barcelona are pretty booked up for July, so I'm thanking my lucky stars I reserved - you can do it through TP's hostel listings with only a minimal deposit on your charge card.
There is PLENTY to do during the day in London. I'm sure you're well aware of all the major tourist attractions (if not, just look at pretty much any page about London).
The first day, take one of those hop-on/hop-off bus tours to get the lie of the land. That way, you know where everything is for the rest of the trip. If budget is a concern, you can get on a double decker bus headed for Victoria, change to another one headed east into The City (or if you start in the East, go westward), and you'll see much of London from above ground. Having familiarized yourself, you'll be able to get around very easily on the Tube the other 4 days and know where you're popping up from underground. (The tube map is not proportional, so it can be disorienting.)
I just remembered - I put up a London travelogue last year that you can read for points of interest... It's more drinking than siteseeing oriented, but who knows, you might get ideas: