Trip from London to Tuscany

"Also, is there anything I should know about driving in France, Swiss and Italy?"

Yes, lots. Since you are driving from the UK, I am guessing you have a UK licence, and a UK registered car. That makes things easier as your licence is valid throughout the EU and you don't need any special documentation for the car (both may change after Brexit). But make sure you have your licence and docs (registration, insurance) with you in the car at all times.

The AA has an excellent set of notes listing where the law in each country is different from UK driving law. See here: https://www.theaa.com/european-breakdown-cover/driving-in-europe/country-by-country

France has tolls on their autoroutes, you pay by distance. Italy has tolls on autostrada, also by distance.
Switzerland has tolls on Autobahn/autoroutes/autostrada, but you pay per year. You buy a sticker called a Vignette, which you stick to your windscreen to prove you have paid. You can buy it at the border, cost CHF 40.

There are two ways to cross the Alps in Switzerland. Long Autobahn tunnels under the Alps, or over the top via passes. The latter is slower and a harder drive, but much more scenic.

Your post just raises so many questions in my mind, and driving in Europe is a huge topic in itself. I suppose your schedule is doable, some 6 hours of driving per day.

For France, paying for tolls and gas has some tricks unless you can find a manned booth and pump. You also need some basic safety equipment, vests, maybe a alcohol breathalyzer. For Switzerland a Vignette. Of course lots of speed cameras, keep in mind no 10 mph over "grace" buffer, 1 km over is speeding. Of course in Italy you have the dreaded ZTL zones that can rack up fines. If a US citizen an IDP, That sort of scratches the surface.

I am still thinking about insurance, is this a rental? a Lease? your own car? a right hand drive car? Why drive? How does this fit into a larger trip?

Thanks for the responses. In terms of logistics i take it all on board. I was wondering more if somone had driven the route before, and what was the best route and places to stay?

I have driven from London to Venice, however that was many years ago. I now choose to drive "slower" in order to avoid our trips being a blur. And not driving a right hand drive car on the continent would also be preferred.
We started by visiting Amsterdam before driving through Cologne and spending the night in Koblenz, Germany. Then we drove on into Munich for a couple of nights. Then Innsbruck, through the Brenner Pass and down to Venice.
At the time, we were just a couple of Bohemian single men looking for a great time.
Today, I'd be flying on a budget airline like EasyJet.com into Pisa. Then catch a one hour local train into Florence. Tuscany is a place best seen by rental car.

I drive to Italy from the East Midlands once or twice a year, most years. I done it as far as Campagnia and usually go to the outskirts of Venice where I can base and leave the car as I take the train to Rome.

Remember that Eurotunnel (I am a ET Frequent Traveller) has increased the required check in time, and between API and tighter border control at both the UK and French queues you need every minute of the increased time. They have been having more equipment problems recently so don't have such a tight timetable that if you are delayed a couple of hours you will be all stressed. There have also been difficulties with French border staff because of their terms and conditions - blaming Brexit - so that sometimes adds time, sometimes lots of it.

Still, I prefer to go under than over.

Do you need to charge your car before getting on the train?

You don't give any hint of your budget for hotels or food, nor what you want to see.

There are many routes and when I go I usually take around a week, stopping for days at a time on the way.

Depending on where you are starting from and how early in the morning you are crossing, Luzern is easily reached in one day. Sometimes I stop in Reims or Châlon-en-Champagne, other times Luxembourg, and often Deidesheim or Neuenkirchen.

All depends.

If I were leaving from Luzern I would go a lot further than Milan or Como, either all the way or perhaps Bologna.

But again, with such little information I can only say where I go - knowing nothing about you or your likes or dislikes.

Why do you think of Champagne, Luzern and Como?

How do you mean "like to see a bit of the Alps on the way"? Off in the distance, or driving through an Alpine village or getting out and hiking?