A supporter outside the court, Nyambura Wainaina, whose mother is Mau Mau, said she was “elated”.
“The most important thing is that the truth is going to come out at last,” she told AFP.
“The British made our people look like barbarians but they were fighting for their rights and their dignity,” she added.
The British government accepts that British forces tortured detainees but said it was “disappointed” with the judgment.
It warned of “potentially significant and far-reaching legal implications” but pointed out that Britain’s relationship with Kenya had moved on since the colonial days, stressing “our people to people ties are and will remain strong and deep.”
The case will have access to an archive of 8,000 secret files that were sent back to Britain after Kenya became independent in 1963.
London had initially argued that all liabilities were transferred to the new rulers of Kenya when the east African country was granted independence and that it could not be held liable now.
But in 2011, a High Court judge ruled the claimants did have a valid case.
The government then claimed too much time had elapsed since the crimes, but Judge McCombe concluded on Friday these claims were “more illusory than real.”
The Kenyans are demanding an apology and the establishment of a welfare fund to ensure that around 1,000 surviving former detainees can have some dignity in their old age.
At least 10,000 people died during the 1952-1960 Mau Mau uprising, with some sources giving far higher estimates.
Tens of thousands were detained, including US President Barack Obama’s grandfather.
In one document sent in 1957, an official in charge of detainees told a police commissioner how prisoners were “beaten up” and made to run around in circles with a bucket of stones on their head if they refused to swear an oath.