In October 1964, a young man was driving to a dance in Hamburg, Pennsylvania, when his radio began to pick up a strange frequency. At first he thought it was just tuning in to a local channel, but then voices came through discussing some kind of nuclear war – and issuing bomb reports.

Recalling the incident decades later, the driver described the simultaneous appearance of a star overhead followed by the sudden realisation that he could see through the floor of his car.

‘I hadn’t done any dope, I wasn’t doing any beer,’ he adds so casually that you feel inclined to believe him. And yet his body felt like jelly. The episode only lasted what seemed like five or ten minutes, but on arriving at the dance, the man realised that the half-hour journey had actually taken nearly two hours. He never found a logical explanation for what had happened.

Between 1980 and 1992, a Cornell graduate from Ohio named John P. Timmerman travelled across America with a recorder and case of cassette tapes. Diversifying from his day job as the owner of an air-conditioning business, he spent his weekends conducting interviews in shopping malls as a volunteer for the Center for UFO Studies. In each mall he visited, he asked shoppers whether they had ever experienced anything inexplicable. The jellified driver was just one of nearly 1,200 people he spoke to across the course of his peculiar career.

We Are Not Alone, which airs on BBC Radio 4 this Sunday evening, replays a selection of these interviews in one continuous stream. There is no introduction – and no explanation – and the only interruptions during the programme are the clicks of a tape ending, the ‘this is side two, cassette one’, type markers made by Timmerman himself and, in the final three minutes, some appreciative reflections from Timmerman’s son. I became quickly hooked.

What struck me, in particular, was how many of the close encounters described took place when people were travelling. Aliens, it would seem, are fascinated by human transport. One woman spoke of a saucer-like object with multi-coloured lights zooming towards her car and disappearing only when another car came into sight. A man with 40 years’ experience in the aviation industry assessed that the sophisticated flying object he saw had no jet engine and was manifestly ‘not from this Earth’.

Many reports released in recent years offer more comprehensive descriptions of sightings than those gathered by Timmerman. But the raw beauty of some of the latter nevertheless astounds.

The captain of a commercial jet summoned the most striking image of the glow he observed while flying north of the Grand Canyon. It was ‘something like the light of the Aurora Borealis’, he recalled, ‘only it was encompassing most of the western sky’. Within it appeared a sphere ‘about the size of a moon when it comes over the horizon’. The moon itself was half-full and directly overhead.

On his journey, Timmerman inevitably encountered some cranks. Top marks go to the woman who informed him that UFOs live inside mountains and only come out at night. ‘How did you know this?’ Timmerman asked her. ‘A lady told me on the bus,’ she replied.

But for the most part, the people recorded were characterised by their wonder and yearning for something beyond what the eye usually sees. The fascination you hear in their voices is as captivating as the stories themselves. The programme will leave you gazing skywards.

You can listen on Radio 4.