If you enter land against the wishes of the landowner, or if you stray outside an area to which you are allowed access, or if you use land in a way which you are not authorised to do, you become a trespasser. Ignorance of that fact is no defence under this law.
Any person can enter a public place, because the landowners permit it. However, this does not make a permanent right of access, and therefore it is within the power of the landowner to ask any person to leave, assuming they do not have some other lawful reason to be there. The landowner does not have to give a reason. If the person does not go immediately, by the shortest practical route, then they are trespassing. Despite the well known sign "Trespassers will be Prosecuted" trespass is not a criminal offence, and trespassers cannot usually be prosecuted. They can, however, be sued. There is little chance of such a matter ever being so serious as to be worth suing over, and so this rarely happens.
People in a park will often protest (if asked to leave) that it is public land. However the ownership of the land is not relevant. Even if the land is owned by a public body, such as the local council, this does not mean necessarily that they have a right to be on it at all times - they do not. If the place closes at a certain time and a visitor remains after that time, they can then be considered to be trespassing. If a visitor misbehaves at any time and refuses to leave when asked to do so by someone with a right to do so (usually the landowner or a representative) then the visitor could becomes a trespasser because they no longer have the landowner's permission to be there, even if they entered legally.
http://www.naturenet.net/law/common.html
It's some time since I did my law degree, but if memory serves me correctly, it is not a criminal offence. HOWEVER causing any damage (an be careful as some farmers can be very canny!) can result in a criminal prosecution.
The police can only really become involved if there are more than a few people in one place or criminal damage has occured. Unless they are really anal!