Nothing like opening a can of worms is there???
This one could run and run (and has done several times before) but there are a few basic rules:
1. As long as your vehicle is legal (ie, properly taxed, insured and MOTd) and as long as only your wheels are on the ground (ie you are not camped) and as long as you are not breaking any other rules (obstruction etc) then you are legally parked. There are no laws that prohibit you falling asleep in a parked vehicle.
2. The Highways Authority (usually the Secretary of State in relation to trunk roads and the County Council on other roads) has the right to restrict parking (including on the basis of weight/height etc) through Road Traffic Orders, so they can prohibit, for example, overnight parking on the edge of the highway or in car parks. NB many local authorities put up prohibitive signs without the force of a RTO behind them, and it is rarely clear which is which without taking up a lot of your time to find out.
My general rule (not the law) is to park up where I won't be annoying people. If there is a notice (whether or not it has the force of law behind it) then I tend to avoid that area because there will probably be someone who will complain and then our reputation goes out the window (the reputation of wildcampers, that is). If we don't annoy anyone, they will probably leave us alone - others will most definitely not agree!