Despite being imprisoned in Palestine and Belgium for his activities - including an attempt on the life of the British high commissioner - Mr Levstein was able to send operatives into the UK who smuggled in explosives.
One of his accomplices, Robert Mishrani, a French student, was linked to an attempted coat bomb attack on the Colonial Office in London in 1947.
The MI5 files confirm there was no evidence that they had detected the plot.
In the wake of the attempted attack on the Colonial Office and a letter bomb campaign against British politicians, MI5 attempted to place known Jewish terror supporters under surveillance.
In one internal memo, an MI5 officer wrote: “These terrorists are hard nuts to crack.”
The Stern Gang - also known as Lehi - was founded in 1940 and openly stated its belief that terror could evict the British authorities from Palestine to allow unrestricted Jewish immigration and the founding of Israel.