The soldiers were members of the Jewish Brigade, part of the British Eighth Army, which fought with distinction in northern Italy in the latter stages of the war.
As the conflict in Europe ended, the Jewish soldiers started their own mini-war. They formed "revenge squads", and with the help of their British Army credentials travelled around Germany and Austria searching for men responsible for the Holocaust.
The brigade's officers and NCOs were British Jews - Edmund de Rothschild, scion of the banking dynasty, was a young captain - but the ranks were filled with Jewish volunteers from Palestine, and refugees who had fled Nazi-occupied Europe.
The hitherto untold details of the story have emerged in a new book, The Jewish Brigade: An Army with Two Masters, by author and historian Morris Beckman. He told the Independent on Sunday: "These were the first post-war executions of selected top Nazis. There were several dozen revenge squads operating; the highest estimate of executions was 1,500. The exact figure will never be known."
Secret orders from Zionist leaders in Tel Aviv instructed members of the brigade to ensure that at least some of the senior members of the SS would be punished for their crimes against humanity.
Working under the codename "Operation Judgement", brigade members formed secret killing squads. In the book, one of the executioners, Israel Carmi, explains how they dealt with their selected targets. "When we arrived at the home of our suspect we would put on [British] Military Police helmets with the white band and police armlets. Then we would enter the home and take the suspect with us, saying that we wanted him for interrogation. Usually they came without a struggle. Once in the car we told the prisoner who we were and why we took him. Some admitted guilt. Others kept silent. We did the job."
Those who volunteered for the killings had lost their families and communities in the Holocaust and were burning with hatred. "We were young Jewish soldiers," one recalled. "We knew that our people would never forgive us if we did not exploit the opportunity to kill Nazis."
British-born soldiers did not take part in the revenge killings, but provided practical support, such as forged papers. Londoner Mark Hyatt, who was an NCO in the Jewish Brigade, told the IoS that he provided the hit squads with "logistical support".
He said: "We did what had to be done and there was no compunction about it."
He had transferred from the ranks of Eighth Army, with which he had fought in north Africa. He summed up the Jewish Brigade as a "very unorthodox outfit".
As well as the execution of the suspected SS and Gestapo war criminals, the brigade assisted tens of thousands of concentration camp survivors to reach Palestine, despite the fact that the British government was implacably opposed to Jewish immigration at the time and that the country was the subject of a naval blockade.
The brigade also gave the Palestine-bound refugees military training and stole, from the British Army stores, thousands of weapons to help arm the Haganah, the embryonic Israeli army.
While the Foreign Office, under the arch anti-Zionist Ernest Bevin, was hostile to the Jewish Brigade and wanted it to be stopped, the British military command refused to act and turned a blind eye to the brigade's clandestine activities. "The commanders of the Eighth Army knew what was going on but they were sympathetic, [as] they had fought alongside the brigade," Mr Beckman said.
Ken Sanitt, an artillery sergeant who had transferred into the Jewish Brigade after four years of fighting in north Africa, Mesopotamia and at Monte Cassino, said: "The British and the Indian soldiers I had been fighting with were elite troops, but they were war-weary, while the Jewish Brigade were spoiling for action. Their fighting spirit was fantastic."
Indeed, the brigade became the template for the Israeli army and 35 former members later became Israeli generals.