Unless you go to the trouble of using an epoxy based product, you will be quite dissapointed. The problem is known, at least here in the U.S. as the
hot tire syndrome. After painting the floor and subsequently parking your car on the floor, the heat from the tires will actually pull the paint in large patches off the floor. The floor needs to be thorougly cleaned, etched with acid and the epoxy based paint applied as directed. Even then, there may be problems but if done according to instructions it should last quite a while.
I would, before painting, take a look at this product:
http://www.bltllc.com/ or one like it. It should be available in the U.K. Good luck!