Catso - on private land, you don't need number plates.
BUT - private land where the general public is allowed access without having to seek permission, such as car parks are very different. You have to display number plates and you can be fined by the police for motoring offences.
The definition of a road in England and Wales is 'any highway and any other road to which the public has access and includes bridges over which a road passes'. In Scotland, there is a similar definition which is extended to include any way over which the public have a right of passage. It is important to note that references to 'road' therefore generally include footpaths, bridle-ways and cycle tracks and many roadways and driveways on private land (including many car parks). In most cases, the law will apply to them and there may be additional rules for particular paths or ways.