Train

It’s possible to get on a train in London and get off the same train in Avignon the next day. Check out RailEurope for more details. If you need it, the phone number of Avignon station is (08).36.35.35.35. Once you are in Avignon, you will need to research car hire for yourself, as I’ve never hired a car from there.
 

You can take your car on the train with Motorail, but it isn’t cheap (around £600-700), and that’s starting from Calais. You still have to get your car there first (see the Driving page for more info). However, if you are coming for more than two weeks, it may be a cheaper option than hiring a car for that period of time.