As it is your first time in Europe I do a few things first while you decide on your itinerary.
- Pick up an RS Guidebook and read it! The Best of Europe is very helpful to first time travelers.
- Look online at a map of Europe and calculate distances between London, Paris and Rome.
- Understand that weather is unpredictable anywhere, anytime so do as suggested and check 10 days out.
And as far as must sees, must try, must do......why are you going?
Because it's there OR because you want to see castles, cathedrals, art, architecture, iconic landmarks, learn a different language, eat different foods. What are your interests and expectations?
A few facts: It will be getting dark by 3:30-4pm especially in London as it's the most northern of the cities you've mentioned.
Currency in London are British Pounds. Currency in Paris and Rome will be Euros.
To get Cheaper trains fares book at least a month in advance especially for the Eurostar between London and Paris.
You haven't mentioned how many days you'll be in Europe but if you are only doing a day and a half in each big city you are short changing yourselves. Drop Rome.
Xmas happenings will be in full swing in London at the end of November. Pantos, the big Christmas carnival in Hyde Park, all the stores will have Xmas window dressings, Christmas lights on Oxford and Regent streets.
Haven't been to Paris for Chistmas for 30 years so GOOGLE to see what's scheduled.