As far as I understand the law, a sign in a layby stating 'No overnight camping/parking' is not legally enforceable unless the county council in question has obtained a Traffic Regulation Order from parliament and, if so, the 'official notice' should cite the reference - example: 'No overnight camping/parking - TRO 1876/10'. Unless there is a specific citation of a TRO, then there is nothing, legally to stop you from resting there. Besides which, even if a TRO is applicable, what is meant by 'overnight' and/or 'stopping' must be specified in that document; even if such a definition does exist, then you are not committing an offence unless you fully comply with that definition - for example, if it states that ' stopping is not permitted between sunset and sunrise' that effectively stops overnight parking but if it simply states something like 'overnight parking is not permitted' then what is meant by 'overnight' is a matter of interpretation and argument - i.e., is 6 hours stopping deemed to be 'overnight' ?(Not in my opinion, and I'm happy to argue the point).
Incidentally, even if stopping is legally prohibited, one can always use the excuse that it is permissible on safety grounds - e.g., you had a migraine attack (if a sufferer and can prove it), or you were simply too tired to continue safely (and slept longer than intended). Note: there is a court case where a man was found sleeping in his car on the hard-shoulder of a motorway in the UK.; he was charged by the police and found 'guilty' of an offence but on appeal to the higher court it was held that he was 'not guilty' (though perhaps unwise to risk his safety) in that he found himself too tired to continue driving to the next off-junction or service station.
Finally, the police do not own the laybys, normally it is the local authority does so it is up to them to get an enforcement order against you (by which time you have left anyway) but even if you are asked to 'move on' and feel that discretion is the better part of valour, then what have you lost? Nothing very much as you can just stop again further down the road.
Oh, I should add that I've overnighted many a time on both the A30 and the A38 without any problems, but please do pick a layby which is set back a bit from the road (for safety's sake ideally separated by a verge or hatching) and not a simple widening at the side of the carriageway which invites other sleepy drivers to tail-end you.
Seannachie.
Of course you could be really wicked and carry a spanner with which to unbolt the sign and toss it into the deepest cover nearby. ;-)