What does British common law state regarding trespassing on private land?

It is Common Law. A civil offence. Trespassers are not prosecuted, they are sued. It applies to all land and rivers over which you do not have right of way and buildings etc thereon. It also applies in certain circumstances to public land. There is no law of trespass in Scotland.

The tort of trespassing on private land is committed when land is entered without excuse and without the express or implied consent or invitation of the owner or lawful occupier. It is also committed when a person, who has lawfully entered upon land with the consent of the person in possession and in circumstances that do not confer on him some interest in the land, refuses to leave within a reasonable time of being asked.