I second the Therm-a-rest mat idea for sleeping on and, when rolled up, they can usually fit behind the seats as long as you aren't' a tall driver with the seat right back. Any decent sleeping bag will pack small and there is plenty of small, light-weight cooking stuff available. Pack everything in dry bags especially clothes and sleeping bag. A boot bag (e-bag) can massively increase your luggage space.
We used to camp for sprints and hill-climbs so we got 2 helmets and race suits in the boot plus tent (3 man Vango tunnel tent), 2 x thermarest, 2 x sleeping bags, 2 x chairs, cooking kit and of course beer and wine. As we are both short we had quite a bit of space behind the seats which helped.