Going to the UK

Depends when in July - I'd personally spend as few days as possible in London (enough to do the tourist sight-seeing schtick) and then get over to Europe.

Early July has the Running of the Bulls in Pamplona which was absolutely brilliant last year - catch the opening ceremony (drunken party) and the first day of running and then move on to either San Sebastian in the north or head south to the main Spanish cities.

Or fly to Rome - spend three days fighting the crowds to see the good stuff, then head north by train to Florence and spend another two days there.

Or spend two days in Amsterdam (where I spent last weekend!) - beautiful city with plenty of entertainment to be found.

Regardless of how you start the trip you want to end it on a beach - either North Spain/South France, North Italy or the Greek Islands. Time it right and you should miss all the lager louts from old Blighty invading the beaches.

Go Camden market on a Sunday, lots of fun to be had.

Get a european rail pass. It can be expensive but it'll afford you the flexibility to see as much or as little of europe as possible. Whoever said it was right, take just a few days to see London as it's not the type of place to really take in the city as it's generally not a particularly nice or friendly place. In fact you'll probably find that the friendliest people are foreign.
Parisians are possibly even less accomadating but you're less likely to be a victim of the great british yob culture as they're far more continental in social situations, whatever that means.
Train it south to Catalonia via the pyranees and check out northern and southern spain before boating it to Corsica or go east dfrom Paris to northern Italy and Milan etc via Switzerland.
Germany's great, Berlin and Munich particularly but that mean a hell of a lot of travel if you want to go to Spain and Italy as they would have to be your top destinations. Italy is fucking great plus if you want to see east europe you can travel to Slovenia and then on to Croatia relatively quickly.
Prague is great but much like Germany it's out of the way.
Basically, get to Paris and travel North, East or South depending on what it is you're looking for from your trip.

Good luck, I envy you.