How long are you going for and how are you planning to travelling between London, Paris, and Rome?
Why don't you consider something like this:
London & Paris Tour — Europe — Contiki Tours and then flying into Rome.
Or, this London to Rome tour:
http://www.contiki.com/destinations/...london-to-rome
Or, if you have the time:
London to Athens Tour — Europe — Contiki Tours
I have done one of these tours before and had a GREAT time! We had lots of free time, saw tons of stuff, and didn't have to worry about hotels and transportation.