Olivier Bancoult, leader of the Chagos Refugees group, said: "We came here in order to ask for our rights, for our fundamental rights, for our dignity as a people, because everyone has a right to live on his birthplace."
Bancoult is one of thousands of inhabitants evicted by the British more than 30 years ago. They were removed after Britain secretly leased the largest of the islands, Diego Garcia, to the United States.
Hundreds of its residents ended up in the urban slums of Mauritius with no money or professional skills.
In a past statement, Bancoult said Chagossians in Mauritius live in the country's poorest regions, faced with "drugs, alcohol, joblessness, prostitution and bad education".
Richard Gifford, the islanders' London lawyer, said returning to the archipelago is "their one hope".
|"We came here in order to ask for our rights, for our fundamental rights, for our dignity as a people, because everyone has a right to live on his birthplace"|
Olivier Bancoult, leader of the Chagos Refugees group
"It's the one thing that uplifts them in the squalor and poverty that they presently live in," Gifford said. "And you can't abandon your culture, you simply have to pursue it until justice is done."
Over the past seven years, the UK's high courts have ruled twice that the people were illegally removed.
But each time the British government has been given permission to appeal.
Chagossians accept that they cannot return to Diego Garcia, now used as a base for US warplanes.
But they do not understand why they cannot live on the other islands in the chain.
Bancoult and his fellow Chagos refugees are confident they will win the appeal.
The foreign office said it would not comment on the proceedings until they are over.
The British government, even if it loses, could potentially take it to the House of Lords, which will prolong the case for years.
The islanders say they will not give up until they return to their "Indian ocean paradise".