The law in the uk is a bit of a mixture that may apply to wild camping or sleeping rough.
Firstly any entry onto private land whether camping or not is a trespass and the owner or agent can demand that you leave immediately, use reasonable force if refuse or ask the Police to help.
There is no legal definition that I know of that describes what a tent is. The word tent appears in several diverse Acts, for example Terrorism Act 2000, Theft Act 1968 or even the Stonehenge Regulations 1997. The former two and similar Acts deal with tents as a dwelling or powers to search therein. The latter allows the pitching of a tent with written permission on the site of Stonehenge. In UK law where a thing is not specifically defined it is a matter for common interpretation i.e. everyone knows what a tent is. I wonder where a system like a hammock and tarp might fit in!
The Vagrancy Act 1935 has some wonderful terms and langauge and sounds quite funny to contemporary ears, but you may contravene this if you wild camp.
Section 1 says:
"So much of section four of the Vagrancy Act 1824, as enacts that a person wandering abroad and lodging in any barn or outhouse, or in any deserted or unoccupied building, or in the open air, or under a tent, or in any cart or waggon, not having any visible means of subsistence, and not giving a good account of himself, shall be deemed a rogue and vagabond within the meaning of that Act, shall have effect subject to the following provisions of this section."
There may also be local bye laws in place for public parks and the like.
My own experience with Police on a couple of occasions is that so long as you are polite and give a reasonable account they will let you be, they will of course wake you up to find that out!
Wild camping is specifically allowed on Dartmoor and in other National Parks over a certain height. see
http://www.go4awalk.com/ask/wildcamping3.php
There is a very good article on a German web site giving similar advice in relation to wild camping in Germany, but in addition it sought the views of a number of Police Officers and Forestry Officers. The article is in German. It is not illegal to sleep rough there but it is illegal to put a tent or shelter up. Most of the officers said that they would allow it if the camper were reasonable when spoken to.
This is an interesting subject and worthy of further study.
I would certainly support the advice regarding litter and leaving no trace setting up late and packing up early.