Whether or not you had an accident only those present or those viewing any CCTV evidence can say.
However, you can be guilty of most of the Road Traffic Act offences (including careless driving, no licence, no insurance, no seat belt etc.) in a car park that is privately owned.
The Road Traffic Acts say that offences are committed if on a road or other public place. Anywhere to which drivers have �unfettered access� (e.g. a supermarket car park, a railway station car park) are �other public places� for the purpose of the acts, regardless of who owns or maintains them.
You are also liable to make good any damage or injury you cause to third parties (either yourself or via your insurers) for any damage or injury you cause, whether on the road, another public place, or on private land.