L,P&R are all big cities and people usually spend a good 5 days to really experience them.  I think you can visit them in only 3-4, but you’ll really have to be on your toes.  Also, I always find it takes at least a day or two to find your way around, figure out public transport, and just feel comfortable in a large, foreign city.   
 
Even though you will probably only spend 3-6 hours getting between cities, you still have to find your way to your hotel and it will cost you about 1/2 of the day. 
 
Basically, your probably going to feel pressed for time for most of your vacation unless you drop a city from the itinerary.  I think Greece is the most logical place to drop, but its completely your choice. 
 
I definately suggest using at least 1 budget flight to get you either to or from London.  Maybe fly to Rome and take trains all the way back, or just the opposite. 

I think you should probably dropped the Greek Islands this time too.  Its going to take you most of a day to get to tehm and most of a day to get back so you really wouldn’t have anymore than a day there.  Spending the extra time in the other cities would probably be a lot better.

Thank you to all of the experienced travelers.  I guess the consensus is that Greece should be off the list.  I had not thought about the time spent finding a way around cities, to and from train stations, etc.  So thank yok.
 
With the remaining cities, how would you fit in Geneva in the itinerary?