On 20 June 1942, the SS guard stationed at the exit to Auschwitz was frightened. In front of him was the car of Rudolph Höss, the commandant of the infamous concentration camp. Inside were four armed SS men, one of whom – an Untersturmführer, or second lieutenant, was shouting and swearing at him.

"Wake up, you buggers!" the officer screamed in German. "Open up or I'll open you up!" Terrified, the guard scrambled to raise the barrier, allowing the powerful motor to pass through and drive away.

Yet had he looked closer, the guard would have noticed something strange: the men were sweating and ashen-faced with fear. For far from being Nazis, the men were Polish prisoners in stolen uniforms and a misappropriated car, who had just made one of the most audacious escapes in the history of Auschwitz. And the architect of the plot, the second lieutenant, was a boy scout, to whom the association's motto "Be prepared" had become a lifeline.

Almost 70 years later, prisoner 918 is holding forth in the home of the scouting association, Baden Powell House in London. At 91, he is impeccably dressed, with a face as wrinkle-free as his well-ironed shirt. As he accepts the ceremonial neckerchief from a shy girl scout from Lancashire, he is as straight-backed as any of the teenagers on parade. In the UK as the guest of a British singer, Katy Carr, who has written a song about his experiences, he is thrilled when the scouts and guides join her to sing for him. Yet in between the traditional trappings of a jamboree, Kazimierz Piechowski, or Kazik as he likes to be called, will tell them a story few in the UK have heard – how, during Nazi occupation, scouts their age were murdered in the streets, while others like him were sent to concentration camps to witness the horror of Hitler's Final Solution.

Piechowski had a happy childhood in the town of Tczew, swimming with friends in the nearby river Vistula or playing with bows and arrows in the park with his two brothers. His family were middle class and his father worked on the railways. When he was 10, Piechowski decided to join the scouts – an act that would alter his life for ever. The youth association was flourishing in Poland, a newly independent state set up after the first world war, with a strong focus on patriotism, "toughness" and brotherhood. "I joined because I was patriotic," he remembers. "And when I arrived home, my mother was crying a little bit and said to me: 'I am so happy you are on the right way.'"

When the Nazis invaded the country nine years later, in 1939, the scouting movement was seen by the invaders as a symbol of nationalism – and a potential source of resistance. "I was 19 when the war broke out," Piechowski says. "Four days after Germany declared war, they arrived in Tczew. They started shooting the scouts." Among those rounded up and killed were Piechowski's childhood friends, and the teenager was terrified. "I knew that, sooner or later, I would also be killed," he says, "so I decided to run away."

He tried to flee across the Hungarian border, a route used by other scouts making their way to France to fight in the Free Polish forces there, only to be caught at the crossing. After eight months in various prisons he was sent to Auschwitz.

"We were only the second transportation to the camp," Piechowski says, "and we had to help build it." The old collection of buildings that made up the original concentration camp was not big enough to house all those caught in mass arrests, so inmates were forced to work 12- to 15-hour days to construct a new camp next door that would become notorious as the Nazis' biggest death camp.

"For the first three months, we were all in complete shock," says Piechowski. And it just got worse. From June 1940 and all through the first six months of 1941, the SS were keen to kill inmates – beating them to death with batons – as the simplest way to cope with the camp's overcrowding. Today, the starvation, unimaginable brutality and physical labour that made the concentration camp a living hell are well documented. But the details of Piechowski's memories still have the power to shock. Inmates were each given a spoon and a tin bowl – not just to eat and drink from, but also to urinate in at night. "If you lost your spoon, you ate from the bowl like a dog," he says quietly. "If you lost your bowl, that was it; you did not get any soup."

Sometimes the guards would murder just to get a holiday, he says. "When an SS man was bored, they would take off a prisoner's cap and throw it away. They would then order the prisoner to fetch it. As the prisoner was running, the officer would shoot them. Then they would claim the prisoner was trying to escape and get three days off for foiling it."

How did people cope? "Some prayed, but some who had prayed before they arrived would say: 'There cannot be a God if Auschwitz exists.'"

For six weeks, Piechowski was set to work carrying corpses after executions. "The death wall was between blocks 10 and 11. They would line prisoners up and shoot them in the back of the head." At the end there would be a pile of naked corpses and Piechowski would take the ankles, while another man held the arms, and throw them on to carts, to transport them to the crematorium. "Sometimes it was 20 a day, sometimes it was a hundred, sometimes it was more. Men, women and children." He looks at me fiercely. "And children," he repeats.

Piechowski as an inmate at Auschwitz

Yet he did not think of trying to escape until a friend's name appeared on a death list. Like many of the boy scouts in Auschwitz, Piechowski joined the resistance movement in the camp. As many of the scouts spoke German, they found useful positions – some were even among the prison police and were able to access the prisoners' files. One day, a Ukrainian friend, Eugeniusz Bendera, a gifted mechanic who worked in the camp's garage, came to him. "He had been told by those who had access to his documents that he was going to be murdered. I was devastated," Piechowski says. The germ of an escape plan formed.

"He said he could organise a car, but that was not enough." The men were being held in the main camp, Auschwitz I, where the fences were covered in electrified barbed wire and there were guards every few metres. The escapees would have to make it through the infamous Arbeit macht frei gate (the legend meant "Work sets you free"), and also break out of the outer perimeter of the complex.

Yet Piechowski could not dismiss his friend's plea. "When I thought that they would put Gienek [Bendera] against the wall of death and shoot him, I had to start thinking." It helped that Piechowski was now working in the store block, where the guards' uniforms and ammunition were kept. Slowly an idea took shape. But holding him back were the consequences for other prisoners. "In the speech the deputy commandant gave when a new transport came in, he would say: 'If anyone thinks of doing something stupid like escaping, let them know this: we will kill 10 people for each person who escapes from a work group or [housing] block.' It was like a cup of cold water hurled over my head."

So that the Nazis would not hold their real working group responsible, Piechowski and Bendera formed a fake group of four, recruiting another boy scout, Stanislaw Gustaw Jaster, and priest Józef Lempart for their "spectacular escape".

On 20 June 1942 – two years to the day after Bendera entered Auschwitz – the conspirators met in the attic of a half-built block to run through the escape plan for the last time. It was a Saturday, when work stopped at midday and the store rooms and motor pool would be unmanned. Before they left they said a prayer for their families, and agreed that if the attempt failed they would shoot themselves. "What was really encouraging us and pushing us on was that if we did not do this Gienek would be killed. "Until the last moment we weren't sure. But we said: 'We have to do this, we have to believe.'"

Picking up a rubbish cart containing kitchen waste, the four started walking towards the Arbeit macht frei gate. Here Piechowski told the guard he was part of a squad taking the rubbish away, praying the guard would not check to see if they were registered. Their luck held and they were able to walk freely out of the main camp and towards the store block. How did it feel? "I did not think about anything," Piechowski says. "I was just trying to pass this final examination. From that moment we did not only need courage, but intelligence."

At the stores, three of them made their way to trap doors covering chutes to the coal cellars. That morning while at work, Piechowski had unscrewed a bolt keeping the doors locked so they could climb in. They made their way to the second-floor store room, broke down the door and dressed themselves in officers' uniforms. Meanwhile, Bendera got into the garage with a copied key and brought round the car.

The mechanic had picked the Steyr 220 – the fastest car in Auschwitz, there for the sole use of the commandant. "It had to be fast, because he had to be able to get to Berlin in a few hours. We took it because if we were chased we had to be able to get away."

They drove to the main gate – passing SS men who saluted them and shouted Heil Hitler. But for Piechowski, the biggest test was still to come. "There was still one problem: we did not know whether, when we came to the final barrier, we would need a pass. We just planned that I would play the role of an SS officer so well that the guards would believe me."

Yet as they approached the barrier, the guard did not move. As he describes what happens next, Piechowski looks away as though he can see the last obstacle before him. "We are driving towards the final barrier, but it is closed . . . We have 80m to go, it is still closed . . . We have 60m to go and it is still closed. I look at my friend Gienek – he has sweat on his brow and his face is white and nervous. We have 20m to go and it is still closed . . ." Bendera stopped the car and as Piechowski stared blankly ahead, not knowing what to do, he felt a blow on his shoulder. It was Lempart. "He whispered: 'Kazik, do something.'

"This was the most dramatic moment. I started shouting." The SS guards obeyed and the car drove to freedom – allowing the men to become four of only 144 prisoners to successfully escape Auschwitz.

The Nazis were incensed, says Piechowski. "When the commandant heard in Berlin that four prisoners had escaped he asked: 'How the bloody hell could they escape in my own car, in our own uniforms, and with our ammunition?' They could not believe that people they did not think had any intelligence took them [for a ride]."

Keeping away from the main roads to evade capture, they drove on forest roads for two hours, heading for the town of Wadowice. There they abandoned the Steyr and continued on foot, sleeping in the forest and taking turns to keep watch. Lempart became ill and was left with a parish priest, while Jaster returned to Warsaw. Piechowski and Bendera spent time in Ukraine before Piechowski returned to Poland, joining the partisan Polish Home Army and spending the rest of the war fighting the Nazis.

In revenge, Jaster's parents were arrested and died in Auschwitz, and there were serious consequences for the remaining prisoners. "A month after we escaped, an order went out that every person must be tattooed [with their prison number]. The Nazis knew that an escapee's hair would grow back, and that the partisans would make new documents for them. But when people saw the number, they would know that they were from Auschwitz. No other camp used numbering – it was our escape that led to it."

Although they were never recaptured, Piechowski relived his time in the camp in flashbacks and nightmares. And his problems were not over. When Poland became a communist state in 1947, he was sentenced to 10 years in prison for joining the Home Army, serving seven. "When I finally came out of prison I was 33 years old. I thought, 'They have taken away my whole youth – all my young years.'"

Later, he became an engineer and when the communist regime fell in 1989, he took to travelling the world with his wife, Iga. He has written two books about his experiences, and tries to ensure no one will forget what happened in Auschwitz. Does he mind reliving his terrifying past? "I am a scout so I have to do my duty – and be cheerful and merry. And I will be a scout to the end of my life," he says simply.

Additional reporting Christina Zaba

For details of Katy Carr's 'Escapologist Tour', which will include screenings of the short documentary Kazik and the Kommander's Car, visit katycarr.com