In a rediscovered 1963 episode of The Sky at Night, Clarke says Russia will win the space race with the US close behind

Sir Arthur C Clarke predicted in a lost BBC interview that the Russians would win the space race by landing the first man on the moon in 1968, probably on the 50th anniversary of the October Revolution.

The late science fiction author made his confident forecast to his friend Sir Patrick Moore in a 1963 episode of The Sky at Night, the world's longest running television science programme. The broadcast was thought to be lost without trace, but has just resurfaced from a television station archive in Africa.

Clarke, who wrote 2001: A Space Odyssey, was introduced by Moore as "a pioneer space research thinker". He was sure the Americans would lag behind the Russians but reach the moon just two years later.

"Around 1970, if you want to pin me down," he said, his native Somerset accent more pronounced than it would be by the end of his life after decades living in Sri Lanka. "The American moon project is a colossal thing, costing $10m a day. I believe they will succeed in getting a man on the moon – and back again, which is equally important – not before 1970, but it will not be much after that."

Moore agreed: "I personally haven't much doubt that the first man will set foot on the moon in the foreseeable future."

It was only two years since the Russians got the first man into space, Yuri Gagarin, in April 1961, but the Americans would get to the moon first.

On 21 July 1969 Neil Armstrong put his left foot down and spoke the phrase which became legendary: "That's one small step for man, one giant leap for mankind."

"We got some right, some not so right," Moore told the Guardian after seeing film of the interview again after almost half a century. "I don't think we did too badly."

The film was discovered in an African television archive by one of an eccentric gang of collectors – finder and exact location firmly anonymous – who scour redundant or obscure archives across the world for lost programmes. Their prime target is lost episodes of Doctor Who, but they recognised the exceptional rarity of the 1963 Sky at Night. The collector who bought it from the archive sent it back, still in its original film can, as a gift to the current Sky at Night production team. Extracts will be seen in the December Sky at Night next week.

The film was particularly moving for Moore as the only record of the only programme which he and his lifelong friend Clarke made live together in a studio. Although he did interview Clarke again, it was through filmed inserts or taped phone interviews.

The Sky at Night began in 1957 when Moore, a writer, musician and passionate amateur astronomer, was invited to fill a hole in the BBC schedule by presenting one live astronomy show a month for three months. The moment Moore lifted one eyebrow and barked an observation straight to camera, a star was born.

In April 2007 the 650th episode was broadcast from Moore's home in Selsey, West Sussex. Moore, frail but dauntless, has no intention of retiring, and plans are being made for the 55th anniversary programme.

Filming was always on a shoestring, with world famous astronomers queueing up to make unpaid guest appearances. Charts fell off walls, string and paper clip models disintegrated, and the reliably unreliable British weather destroyed many outdoor broadcasts including the 1999 solar eclipse.

"Its longevity is certainly down to Patrick himself – and to the time slot," said Mat Irvine, a former BBC special effects engineer (and still the operator of K9 whenever the robot dog pops up on Doctor Who or its spin-offs) who regularly drove to Moore's house with a car boot load of model planets and space probes. "It had to be done after dark, and it always went out at the very end of the night, sometimes toppling over into the next day, just before the national anthem and closedown. It wasn't a slot that anyone else was clamouring for. If he'd had a better slot he'd have been shoved aside years ago."

Jane Fletcher, only the sixth producer in the programme's history, says scores of the earliest programmes are missing. Most went out live, and very few were recorded. Some of those that did survive were wiped, or just thrown away. "They were seen as over and done with, and not having any special importance, so there was no great concern about preserving them."

Irvine believes this one survived because it was filmed as it went out live, and then probably sold to an overseas station.

The man on the moon forecast came at the very end, when Moore challenged Clarke to make predictions about the coming years in space research.

In 1963 Moore and Clarke's views of the Russian space programme were based on inspired guesswork, and occasional reports smuggled out to Moore by friends in the Soviet Union at the height of the cold war.

However, one of Clarke's predictions proved very wide of the mark. There would be a permanently manned space base on the moon, and possibly a man on Mars, "before the end of the century", he said. The world is still waiting.

• The rediscovered 1963 episode will be discussed in the December Sky at Night, transmitted on BBC1 on Sunday 4 December and BBC4 on 8 December.