The Plan
Get a group of people together (3 people per car) and come up with a team name.
Buy a car for no more than £400. Probably a good idea to get one with Tax and MOT and a japanese one for reliability.
Spend however much you want doing it up, ie; putting massive monster truck rims on it, fitting it with an air horn, painting flames/bullet holes on it, or just fixing it up.
Get all drivers insured on it (european cover) and get european breakdown cover.
Drive around a load of places in Europe, stopping off every night at a hotel. Lots of drinking.