In UK law, how can someone claim adverse possession of a piece of land?

My father owns some land which, for some years, a gypsy has been using for his horses without payment or permission. My father has repeatedly asked him to remove the animals, but to no effect. He has even tried to deter the gypsy by getting the land ploughed, but the gypsy intimidated the contractor, who did not complete the job.

The gypsy, through a solicitor, did at one point, offer to enter into a tenancy agreement (which I think would stand up in a UK court as an admission that he does not own the land?), however the gypsy would not agree to the terms that were acceptable to my father, so no agreement was entered into and no payment made.

My father (an 89-year-old pensioner with very little income) now needs to sell the land but cannot while it is occupied. We are worried that the gypsy may claim 'adverse possession'. We hope that he would not have a case because his occupation has not been unchallenged - is that correct under UK law? We are also worried that if he does make a claim he may be able to get legal aid; again, we are hoping that this might not be the case - an answer on this would also be very welcome.

There is no way that my father can afford a massive legal bill. Any advice you can give on this would be massively appreciated - thank you!