During the descent to Earth, the spacecraft’s equipment module, which contained engines and propellant, failed to fully detach as planned.

The cosmonauts were exposed to high G forces as both the equipment and descent modules of the spacecraft started tumbling.

However, the ordeal ended when the cable linking the modules burned through, freeing the cosmonauts’ capsule.

The descent module floated through the clouds on its parachute. It touched down in deepest Siberia, in the middle of a forest of birch and fir trees. Leonov recalls:

 We landed and opened the hatch. The air was cold, it rushed in. We set up our radio channel and began to broadcast our coded signal.”

“Only after seven hours did a monitoring station in West Germany report that they had heard the coded signal which I had sent.”

Both cosmonauts had grown up at the forest’s edge, and understood its dangers.

It was home to wolves and bears, and March was mating season, when the animals were at their most aggressive.

After a few more hours, the cosmonauts heard the unmistakable thud of helicopter blades. They walked to a clearing, where they saw that it was a civilian chopper.

The pilot and crew were keen to rescue them, throwing down a rope ladder. But it was too flimsy for Leonov and Belyayev to climb in their heavy spacesuits. They declined the offer.

The helicopter crew must have told others of the men’s whereabouts. As other aircraft began to circle above them, crews threw all kinds of items out for the cosmonauts: a bottle of cognac - which smashed the instant it hit the snow - a blunt axe and warm clothes, most of which got caught in the branches of the tall trees.

Private aircraft were and are relatively common in Siberia, because of the vast distances to travel.

As it got dark, the cosmonauts realised they would have to wring the moisture out of their suits to avoid frostbite.

Leonov had perspired so much on the spacewalk that his sweat was now sloshing around in the suit, up to his knees.

There was no way to cover the hatch opening, so they would have to cope as best they could as temperatures dropped to -25C.

Leonov remembers that he and Belyayev awoke to the sounds of a rescue party approaching:

 They landed 9km away and came on skis. They made a little hut for us and brought us a big cauldron which we filled with water and put over a fire. Then we washed in it.”

The men had to spend another night in the forest, but this time it was in the more comfortable surroundings of their new log cabin.

The next day Belyayev and Leonov donned skis for the 9km journey to a clearing where a helicopter was waiting to fly them to the city of Perm. Leonov recalls:

 When we flew out of there, the rescuers said they saw wolf tracks around the spacecraft.”

“Wolves are very smart, they came to look at what had come down from the sky into their territory.”

From Perm, the men were flown back to Baikonur, where they were greeted on the runway by Korolev and Gagarin.

During a mission debrief, Leonov had to explain why he had broken protocol by venting his air into space without telling ground control.

He responded: “What would you have done if I’d told you? You would have created a commission. The commission would have selected a chairman, and the chairman would talk to me.

 I knew I only had 30 minutes left and I didn’t want ground control to panic.”

Sergei Korolev, the chief space designer, backed him, saying: “Alexei is right.”

After the cosmonauts returned, the authorities said nothing to the press about the problems encountered on the mission.

It took many years for the truth to emerge about the first, historic spacewalk mission.

For years, the Soviet space programme was seen by some in the West as a less sophisticated pretender to Nasa, whose achievements in the era of the Moon landings are viewed as a high bar in the human exploration of space.

But it was the space pioneers of the Soviet Union who blazed a trail - taking risks, making mistakes but ultimately pushing the boundaries of human knowledge.

“If there are some people who think that what we did was primitive, not very interesting, not worthwhile - let them fly into space, go for a spacewalk and experience the air leaking from your suit, or a safety hatch refusing to shut,” says cosmonaut Georgy Grechko.

“Then they will understand that our pride and happiness is deserved.”