As others have said, you'll get by with english, but knowing a few words of french and italian may make your trip more interesting. Tour companies and organised trips are good if you want to cram a lot in, but it can be tiring getting dragged around. The London/Paris/Rome No.1 must-sees for me would be Westminster Abbey/Eiffel Tower/St Peter's. The best show in London IMO is Billy Elliot (but I'd recommend you have a quick look at Margaret Thatcher/miner's strike on Wikepedia beforehand to understand the context). If you've got time to travel out of the cities then Oxford is lovely and an easy trip from London while Versailles is spectacular and only just on the edge of Paris.
Enjoy your trip!