The agreement, which includes a plan to lease back the strategically important US military base on Diego Garcia at British taxpayers' expense, is opposed by the Conservatives who fear China's influence in the region.
Ms Dugasse and Ms Pompe say the islands should remain British.
They want the right to return to live where they were born after Chagossians were forced to leave the Indian Ocean territory by 1973 to make way for the base.
image [https://cdn.magzter.com/1583504377/1742173784/articles/CrPfCvkURi83KHlzh4sys/1747167784.jpg]
Lawyers for the two women have sent a pre-action letter to the Foreign, Commonwealth and Development Office.
They claim the Chagossian people have unlawfully not been given a say in the future of the islands, despite being the native inhabitants.
They also say that they do not trust Mauritius to treat the Chagossians fairly as they would not hold Mauritian nationality. They fear they will never be able to return.
Ms Pompe said: "Chagossians were removed from their place of birth, without their consultation, and have been treated badly for 60 years.
Suffering
"Since then we have been struggling to understand why we have been treated so poorly by the British Government.
"Our human rights have been stripped away. Today the British Government is repeating the same mistakes which it made 60 years ago. All our suffering and cries to be heard have been falling on deaf ears. I want to stay...