The group, seeking compensation at the High Court, allege they were assaulted between 1952 and 1961 by British colonial administration officials.
Thousands were held in camps by the British during the uprising and many were tortured or killed, say activists.
The government says too much time has elapsed since the alleged abuses.
It says it cannot be held liable.
The legal action is being brought by three Kenyan men and one woman, all of whom are in their 70s and 80s.
Their lawyers say that the four represent the wider community of Kenyans abused during the rebellion against colonial rule in the 1950s.
They say there was systematic use of violence against thousands of detainees involved in the rebellion or suspected of supporting it who were held in detention camps.Continue reading the main story A guerrilla group known as Mau Mau began a violent campaign against white settlers in 1952The uprising had been put down by the British colonial government by 1960The Kenya Human Rights Commission says 90,000 Kenyans were executed, tortured or maimed during the crackdownIt says 160,000 people were detained in appalling conditionsKenya gained independence from Britain in 1963The movement is widely thought to have helped Kenya achieve that independenceThe Foreign Office says it understands the strong feelings the Mau Mau issue still evokes and that the period caused a great deal of pain for many on all sides.
However, it says the UK intends to fully defend the cases, arguing that the government cannot be held liable.
Archive searches connected with the case have led to the discovery of thousands of files from former British administrations, including Kenya, which the Foreign Office is to make public.
The armed movement began in central Kenya during the 1950s with the aim of getting back land seized by British colonial authorities.The background to the case
Historians say the Mau Mau movement helped Kenya achieve independence.
However, their actions have also been blamed for crimes against white farmers and bloody clashes with British forces throughout the 1950s.
The Kenya Human Rights Commission has said 90,000 Kenyans were executed, tortured or maimed during the crackdown, and 160,000 were detained in appalling conditions.
An official report in 1961 determined that more than 11,000 Africans, most of them civilians, and 32 white people died during that period.
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