The three Kenyans won a ruling from Mr Justice McCombe last year that they had "arguable cases in law".
But the case came back to London's High Court in July to consider a claim by the Foreign and Commonwealth Office that the actions were brought outside the legal time limit.
Lawyers for Wambugu Wa Nyingi, Paulo Muoka Nzili and Jane Muthoni Mara argued that it was an exceptional case in which the judge should exercise his discretion in their favour.
Today, Mr Justice McCombe said they had established a proper case for the court to exercise its discretion and allowed their claims to proceed to trial.
More top news
A man and woman have been arrested on suspicion of murder after a badly burned body was found in a garden in Southfields, south-west London.
Kim Jong-un has called Donald Trump "deranged" and says he will "pay dearly" for his threats, according to North Korea's state news agency.
Theresa May will tell European counterparts their shared political legacies depend on agreeing a good Brexit deal.