Unauthorised encampments on land you own
Trespass is not a criminal offence, it is a civil matter and so the police don't usually have powers to deal with unauthorised encampments. There are exceptions to this, for example, when the encampment is over a certain size, or if there are other policing issues associated with the encampment. The police work very closely with the council to help manage unauthorised encampments and, when appropriate, will take action to deal with problems that may arise.
Landowner is allowing an unauthorised encampment to remain temporarily
Unless the landowner has already obtained planning permission or is a farmer and the campers are helping with temporary labour, such as fruit picking, the landowner could be in breach of planning law and the laws dealing with the licensing of caravan sites.
Landowners not taking action to remove unauthorised encampments
If the landowner will not take appropriate action to remove the encampment, and there is a breach of planning or licence requirements, the local planning authority may take action against the landowner to require the removal of the caravans. Court action would likely to follow if the landowner does not comply.
Gypsies and Travellers setting up an encampment on land they have brought
Any individual who wants to live on a piece of land needs to obtain planning permission and Gypsies and Travellers are no different.
If planning permission is not granted and caravans are set up on a piece of land, even if it is privately owned, then it can be classed as an unauthorised development and the local planning authority can deal with it under normal planning powers.