HGV drivers can do it because they can't be forced to drive on if their hours are up. Car drivers aren't restricted so can be forced to move on.
In England & Wales - laybys are part of the highway. You can park but must have lights on the car and caravan overnight and be prepared to move on if requested by police or highways agency officials. In Scotland the law is different, you're less likelky to be troubled but I'm not sure of the rules.
The main problem with laybys is the buffetting from HGV's. Even laybys on old sections of road, now bypassed, seem to generate enough traffic to give frequent disturbance.
The problem with CLs is that you can't arrive at 11pm and leave at 7am.
We've also tried supermarket carparks, eg Tesco Carlisle, but there's too many vehicle movements to allow a decent rest.
We've tried many different ways to tackle this problem, usually without success. The only one that works for us is to stop in the early hours of the morning on the A82 along Loch Lomond en route from the Midlands to the North-West Highlands. The breakfast view is fantastic and we can clear the narrow section of the A82 before the coaches get there.