I've never seen a 'parent & child' space on a public road, so I suppose you must be referring to supermarkets.
It's not illegal (under the normal parking laws) to park your car on either the 'disabled' or ''parent & child' spaces on a supermarket car park. It is, however, illegal to drive a motor vehicle over private land without permission. While I think that it's extremely unlikely that a prosecution would be brought using this legislation, it could be argued that a 'parent & child only' notice was a sign indicating that drivers (without children in their cars) did not have permission to drive on that part of the car park.
Some supermarkets are 'getting tough' with drivers who flout their rules (by, for example, banning them from the store) but it's unlikely that anyone would actually be fined for doing so.
Anyway, are you really so lazy that you can't walk from the far side of the car park?
Chris