Best route to visit Paris, Zermatt, Rome, Florence and Venice from London

Think about this:

1. Land in Paris
2. Paris --> Geneva --> Zermatt combination of trains
3. Zermatt --> St. Moritz Glacier express which is one of the world's most beautiful trains
4. St Moritz -->Venice-->Florence -->Rome Italian train
5. The travel within Italy can be done in Italy Rail pass
6. Fly out of Rome

In general, you can use the website raileurope.co.uk for train bookings. However, Glacier Express needs to be booked separately.

Easily the best way to get to Paris is utilizing the Eurostar train from London. You can get there in less than 3 hours. I based out of London when I studied abroad and we utilized all the discount airlines for Rome and Florence we actually took the train from Venice to Florence which was nice. But it's also easy to get flights from London. Be sure to note which London airport it is though. A lot of the discount services fly out of London Luton Airportor London Stansted Airport (STN) which is fine, but can add in significant travel time as they are not located in London proper. 

Paris - Zermatt. You'll want to take a day train on this route our you'll miss the scenery. You'll go via Zermatt and Visp with two changes. Not enough time on any train to sleep overnight.

Same from Zermatt to Rome. Go via Brig and Milan.

No night trains on the short runs within Italy. There are direct trains between your destinations.

Buy your Eurostar and French trains now to get the best prices. Look up schedules at ban.de

Take the chunnel train from London to Paris, the London train station is easy to get to and you will arrive in Gare du Nord Paris in 3 hours.  With the exception of being in the dark inside the tunnel, this is a smooth and interesting ride across France.

From Paris, take the train to Rome, which would be the furthest city south that you have described.  You are going to need to examine a train schedule to determine what will meet your requirements, but I can assure you that European train service is frequent, reliable & fast!

Rome to Florence, again by train.  The Florence train station is in the middle of the city, so getting to whatever hotel you have selected, will be simple.

Florence to Venice by train is also straight forward, cars are not allowed in Venice, but the train station is on the first main island, so from there, you can easily walk to your hotel.  Be careful when you make these reservations, you do not want to go to Mestre, which is on the mainland, you want the train all the way to the island.

Also be careful with the train from Venice to Zermatt, some take as long as 17 hours, but the faster express trains take 12 hours.

Most European trains have multiple levels of service, but to keep your costs down, bring your own snacks and drinks.  

Unless you want to cruise through these countries and spend most of your time driving/riding, I would really encourage going deeper in one place/area. Paris and out trips in every direction would be heavenly.