The definition of “other public place” for the Road Traffic Act is usually interpreted as a place to which the public have unfettered access (with the rider “during opening hours” if applicable). So for example, Tescos car park would fit the bill, but a private (e.g. office) car park which restricts entry to, say, staff with a permit, would not.
Ambiguities arise in this definition however. What if the car park is open to all but is gated and access only allowed by an attendant who opens a barrier? What about Tescos car park when the store is closed and the car park gated?
Not sure about the NEC or how it operates but I would imagine they have looked into it.