A council has taken exiled islanders who have protested outside its offices since August last year to court to apply for possession of the land.
Islanders have been protesting outside council buildings in Sussex
The group outside West Sussex council offices in Crawley want the government to let them return to Diego Garcia, which became a US airbase in the 1970s.
Lawyers for the protesters said the council served a notice in September ordering the group to cease occupation.
Summing up, a Brighton County Court judge deferred judgement to next week.
The protest group, the Chagos Island Community Association, said conditions had deteriorated over Christmas because of the cold and because the social services building where the group use facilities had been closed.
Protesters living on a covered, paved area immediately outside the front door of the council offices have brought with them seats and settees, and stocks of banners, food and water. None of them has a tent.
Families were exiled from Diego Garcia, in the Chagos Islands, in the 1960s and 70s to make way for a US Indian Ocean airbase, and had to leave for Mauritius.
Many ended up in the UK and settled near Gatwick Airport in Sussex when they landed in the country.
The group's lawyers said about 400 islanders now lived in Crawley.
In a separate case last May, the High Court backed the islanders who claimed they were illegally removed by the UK Government.
The Foreign Office claimed the government acted within its powers and did not accept that any residents of the territory were unlawfully removed.
That legal action was brought by Louis Bancoult, leader of the Chagos Refugee Group, who was evacuated from the islands as a boy.
The government was given permission to appeal, which is expected to happen in February.