Road Trip through EU starting in London

If you plan on drivning on the continent, just rent the car in France, no one says you have to stick to one mode of transport. Make sure you know the pros and cons of driving in Europe. A car is great for rural travel, but a pain if you plan on going to major cities and for long distances.

1) Possibly with the bigger car hire companies. I suggest you ask them if they have LHD cars.
2) The car should have all the necessary documentation with it. But, if your Driving Licence is from outside the EU, you will need an IDP (International Driving Permit) as well as your licence to drive in some countries.

3) Yes:
a) Where are you planning to return this car? Hiring a car in one country, and returning it in another incurs a large surcharge £££€€€.
b) Crossing borders is usually no problem (check before hiring), but taking a car on a ferry may be forbidden or carry extra insurance - ask.
c) You can take a car through the Channel Tunnel - a lot faster than a ferry: https://www.eurotunnel.com/uk/home/
d) How long is this trip? Are you aware of the "90 days in any 180" limit for non-EU/Schengen citizens staying in the Schengen Area?
e) Are you aware of road tolls. Some countries have tolls on Motorways/Autoroutes/Autostrada/Autobahn, some have "Vignettes" where you pay tolls by the month instead of per Km, some are free.
f) For routes, including times and costs (fuel+toll), use: https://www.viamichelin.com/ The times assume no stopping, add 25%-50%.

One suggestion. Hire a UK car for touring the UK, then when you want to go to "the continent", hand it in and take a Eurostar train from London to Lille, pick up a French car there. Lille is easier driving than Paris. After your Grand Road Trip, loop back to France, and hand the car in back in France.

It's most common to book separate cars for the UK and the continent, and save the cost of transporting the car, and not have a car "in your way" in either London or Paris. You certainly don't need to drive from London to Paris if you're not using the car more in the UK.

The French car leasing programs for visitors (lasting 3 weeks to 6 months) do offer pick-up in London and drop off in France or selected cities in neighbor countries. I did this with no problem several years back for a 6-month lease (before Schengen stay rules tightened up). I enjoyed driving the LHD car in Britain and Ireland, although a single driver has trouble any time you go through a drive-through or need to take a parking ticket from a toll gate on the other side of the car.

Regular, passenger-only Eurostar train tickets from London to Paris range from $65-200 per person in Standard class. Book early to get one of the better fares, probably in the middle of that price range for this summer.

Hi, prefer to rent a car. It is more convenient and comfortable, as you can move the place you want to visit.

Renebaker your statement is a bit nonsensical. Have you driven a car in Europe before? A car is not always more convenient or practical, it depends very much on where you plan to go. If you want to go from London to Paris, to of the most congested cities in Europe, then a car is in no way convenient.

1 - Highly unlikely from your common or garden car hire. Take train / plane to your first country after the UK. The easiest way to do this might be under one of the car company leasing arrangements I guess as mentioned above.
2 - You will need to have insurance coverage for all countries. Check on need for IDP.
3 - You will need to have the legally required equipment in the car for each country you pass through - by default it will be legally set up for the country of origin. Unless you like paying massive drop off fees, return to country hired in.

Assuming you trip is longer than 3 weeks you can do lease with Peugeot or Renault and the car will be LHD. ( lease cars are sold off as used cars in France as soon as you return them) There are pick up and drop of fees outside of France. The chances of getting an LHD car through a rental company are somewhere between Slim and none on the off chance that Slim is in the UK. The last time I rented a car in Europe was in 2006 against the advice of a good friend and I will NEVER make that mistake again unless forced to by time constraints.

Driving an LHD car in the UK is not that bad, if you have a navigator in the right hand seat. Mainly need to remind you to Keep left after making a turn and to tell you if it's safe to pass a truck or bus on a two-lane load.

My advice is do not drive in London or Paris, stay on the outskirts and commute into town to see the sights. Between restricted travel zones and traffic in general it is not worth the effort.

The rental or lease car should come with all the paperwork you will need for the vehicle. On a personal basis, an International Driving Permit is strongly recommended in France and mandatory in Spain.

You want to take a GPS that you know how to use with a European map card in it and some good paper maps to back it up. The GPS is great for telling you where you are on the micro scale but the tiny screen does a lousy job of telling you where you are on the macro scale.