Euro Rail Pass or buy individually

You will be able to buy these with nonrefundable tickets now for a whole lot less than the cost of a Eurail pass. In addition, each of these will require extra cost for separately purchased seat reservations with the Eurail Pass. Seat reservations are included in the price when you buy the tickets outright.

Please read this webpage: https://www.seat61.com/Europe-train-tickets.htm
And this one: https://www.seat61.com/Railpass-and-Eurail-pass-guide.htm#railpass-or-point-to-point-tickets

The whole website is the ultimate resource for train info (or more exact where to find train info).

• Yes, you should buy advance purchase (discounted) tickets for each leg, same as you would for flights, with the difference that train prices only ever go up as you get nearer the travel date, they never go down.
• Buy direct from the companies running the trains (different company for each of your routes).
• You probably need 2 more train trips: arrival airport to Florence, and London to departure airport.
• For Paris and London you need to research local public transport to get you around those cities, London tube, Paris métro and buses in both cases.

Finally, and most importantly, enjoy your trip!

You don’t need a Eurail Pass for your simple journeys. Buy point to point tickets.

www.trenitalia.com
www.sbb.ch/en

OR

a reputable 3rd party seller is www.trainline.eu

The price comparison will depend on how far in advance you're actually booking the trains, since the best prices have limited seats available. If you're booking now for travel more than a month away, advance-discount tickets will probably be cheaper. If you're traveling before the end of May, the rail pass plus reservations can be cheaper ($246 for 3 days in 2nd class, plus about $70 for 4 seat reservations, versus ticket prices currently for sale could easily add up to $450).

If you buy nonrefundable tickets now, you will save money over the Eurail Pass. For random dates in August:
Florence to Luzern, 60 EUR ($67)
Luzern to Paris, 67 EUR ($75)
Paris to London, $65

So that is about $207. But you have to buy the tickets now. Prices only go up, and they are train specific, just like airplane tickets. If you want to remain flexible, as Laura pointed out, it will cost about $317 with a Eurail Pass.

But the advantage of the Eurailpass is that you don't need to do the advance ticketing.

Keep in mind that adv discount tickets are fine if your paramount concern is to save on the expenses. Getting those tickets means you've locked yourself in to a specific time of dep and train., sacrificing any flexibility.

I use a Pass but with you itinerary I would not advise getting the Global Pass, trip is too short, rides are too few, not enough zig zag traveling....on your trip get the individual tickets.