Few bits:
-Scotland
Wild Camping is fine, but NOT vehicle camping. Wild camping in Scotland, under the
Scottish Access Code, is permissible but it is intended to be lightweight backpacking type camping. ie if you park the car in a layby and walked 20m or so from the vehicle and set up camp there it wouldn't be a problem (except for certain areas)
I've seen cars parked at the side of a main road, and then a tent on the other side of a farmers hedge!
-England
Low level wild camping is a bit of a challenge; there isn't that much land accessible really; as Ben and others have said the Forestry Commission stuff is the best bet. In the New Forest I'd not bother; have a look at the Forest Enterprise sites, there are some smaller ones there but it's so popular that it's hard to wild camp (although I have as part of my Duke of Edinburgh's Award expeds as both a leader and a participant, but that's done with full consent on specific sites that are agreed with the councils)
The rule for walkers is (unofficially) above the last fence line on the high level routes; typically this is above about 500-600m and is often the case in the Lakes, Peaks etc.
Exmoor, Dartmoor etc I'm not so sure on as I've not used those areas.
-Wales
Very much the same as England; there's the same access legislation (
CROW Act 2000) so much of it is the same.
There are some good wilder official campsites around in Snowdonia; Gwn Gof Uchaf and Gwn Gof Ilaf (next to one another) are both pretty wild, but do have facilities.
I suppose to sum it up, England and Wales are bit of a minefield, but Scotland is easier... BUT the laning in Scotland is harder because they don't mark on the maps what a BOAT is any longer (perhaps find an older map?), whereas in England and Wales they do. In all cases the easiest way would be to "walk" in with minimal kit, as that avoids the issue of a vehicle being in the wrong place (which in England and Wales could open you up to Trespass prosecution because the argument is that the vehicle has done damage)
Obviously Leave No Trace; if you brought it in, you can bring it out (plus anything else you may find).
Hope that helps, as I think of more I'll add to it.
With regards to the legal side of things; trespass is generally a civil matter, so the Police aren't that fussed... unless you're itinerant workers who have set up a large number of caravan's and deal in scrap metal...