Last year, the trio won a ruling that they had "arguable cases in law", but the Foreign and Commonwealth Office (FCO) maintained the actions were barred as they were brought outside the legal time limit and a fair trial was no longer possible.
But lawyers for Wambugu Wa Nyingi, Paulo Muoka Nzili and Jane Muthoni Mara said it was an exceptional case in which Mr Justice McCombe should exercise his discretion in their favour.
After he announced yesterday that the claims could proceed to trial, solicitors Leigh Day said the Government would face potentially thousands of claims from Kenyans who suffered similar torture.
Senior partner Martyn Day said: "This is a historic judgment which will reverberate around the world and will have repercussions for years to come.
"Following this judgment, we can but hope our Government will at last do the honourable thing and sit down and resolve these claims.
"There will - be victims of colonial torture, from Malaya to the Yemen, from Cyprus to Palestine, who will be reading this judgment with great care."
The FCO is to appeal. A spokesman said the claims of torture were not disputed, but added: "The normal time-limit for bringing a civil action is three to six years. In this case, that period has been extended to over 50 years despite the fact the key decision-makers are dead."