It's mid-afternoon on a busy April day at Gatwick. Passengers with suitcases and bundles are coming and going, jetting in from one part of the world, heading off to another. And on a chilly floor in a ladies' toilet, a tiny baby waits for his life to begin. It was 10 April 1986 – 25 years ago tomorrow. The baby was about 10 days old, according to a doctor who examined him later. He was wearing a striped vest and two babygrows – one blue, one yellow – and wrapped in a blue-and-white checked blanket.

He had been well fed and well cared for. In fact, he was sleeping so soundly that when Beryl Wright, a duty-free sales assistant, spotted him as she was washing her hands, she thought he was a bundle of rags. Only when she moved the outer blanket to one side did she realise it contained a baby.

At first, Beryl thought the baby's mother was in a cubicle; then, she thought maybe he'd been accidentally forgotten. But as she cuddled him outside the ladies, and no one appeared to claim him, the terrible truth began to dawn. The mother wasn't coming back. The baby had been abandoned.

Fast forward 25 years, to earlier this week. We are still in Sussex, but in the seaside town of Littlehampton, 30 miles south of Gatwick, at the home of a likeable, unassuming young landscape gardener, Steve Hydes. Steve is a lovely guy who's proud as punch of his engaging little daughter Alanna, three, and his partner Sammy, who works in a care home. But Steve is a man without a past, because he was that baby in the ladies at Gatwick. And because he's got Alanna, and because he wants her to know who her paternal blood grandparents are – and also because, now he's had a child of his own, it has made him realise how powerful genetic connections are, and also how extraordinary it was that his mother could have abandoned him – he has decided to try to piece together his story. So Steve Hydes – dubbed "Gary Gatwick" by the press after the airport's souvenir teddy bear – has turned amateur detective. And he's on a quest that may be more urgent and possibly more far-reaching – certainly more complex – than most.

We're in Steve's sitting room, surrounded by a pile of faded press cuttings and official-looking police letters, examining the paper trail in the hope of finding that one piece of evidence that could change his future. Steve seems almost apologetic about his search. "I've got a great family," he says. "I'm luckier than most." As well as Sammy and Alanna there are his adoptive parents, Sandra and John, and his three sisters – Stephanie, Joanne and Natalie. He is also close to Sammy's father, Keith, and her mother, Sandra. The thing is, he explains, he lacks a heritage, a hinterland. Most adopted children know something of where they came from, who their blood family was. Steve knows nothing: his known history began at 2.45pm on 10 April 1986. The 10 days before that; the nine months he spent in someone's womb; the relationship that gave him life; the family tapestry into which he should have been woven; all the cultural, genealogical and geographical landmarks that make us who we are and give us identity – all that is missing for Steve.

Everything he knows about himself is what Beryl found that day, on the floor of the ladies'. And it isn't enough. Not now that he has Alanna.

So Steve started his search. He went first to the items his parents had kept for him: the clothes he was found in, the press cuttings and the written testimonials of the people he encountered at Gatwick. Their words, preserved under cellophane in a photograph album, bear witness to the extraordinary effect a helpless, motherless baby has on the adults he or she comes into contact with. One of the policemen at the scene describes how "when all the fuss had died down, Gary was fed by Sergeant Ahmed Ramiz, who had bought the milk himself". Ahmed, the account continues, had three young sons of his own: he asked to be allowed to take the baby home with him that evening, if no foster parents could be found. Janice Stone, the social worker called in, remembers "wrapping the baby in my scarf, because it was so cold". And Tricia Stamer, the airport public relations staff member, describes how "because his romper suit was wet, we dipped into the department's tea money to buy him a new one".

The testimonials moved Steve so much that he decided – with the help of the PR team at Gatwick, who traced the people concerned – to go back to the airport to meet Beryl, Janice, Ahmed and Tricia. When he did, he realised that, in a way, they felt like family. "They knew more about me in some ways than I knew about myself," he says. "What amazed me was how much they cared. Beryl told me she'd thought about me every single day, for more than 20 years." He swallows. "I hadn't expected that."

Meeting the people who cared for him that day, Steve felt he was putting some of the jigsaw pieces of his past into place. But he needed more: what about the 10 days before 10 April? Where were his roots?

Because he was found at an airport, Steve always wondered if his background was non-British. Some of his adoptive relatives speculated that he had an Irish, or even a Russian, look. Poignantly, among his treasures, he has the lists of arrivals and departures into Gatwick on the day when he was found. He could have come from almost anywhere on the planet.

Then he heard of a way to check out his background. "I heard there was a DNA test I could have which would give me some idea of my roots, placing me from somewhere geographically, and maybe even linking me to specific family lines," he says.

He went to Edinburgh, to meet Dr Jim Wilson, a population geneticist at the university there, who analysed his DNA. He shows me a graph: what it reveals is that – contrary to his relatives' speculations – Steve's forebears were probably of English or Scottish descent. Wilson has also done a Y-chromosome check, tracking the male bloodline from that – and the results show that his father's family are more likely to come from the east of Britain than the west.

Finally, and in many ways most fascinating, was that Wilson fed Steve's DNA into a global databank containing the genetic profiles of millions of individuals. These were people hoping to find family matches for either genealogical or medical reasons. From this, he identified a number of individuals who are Steve's seventh or sixth or even, in one case, fifth cousin.

For many people, establishing information so vague and remote wouldn't mean much. Steve felt as if he had been given pure gold. "You've got no idea how it feels to know nothing about what nationality you are, or where you come from," he says. "This is worth so much to me. It places me somewhere, it gives me a place to say I'm from. I'm European; I'm maybe from England. I link in somewhere, even if I only have a vague notion of where. There are people somewhere on the planet who are my very, very distant relatives. And all of it matters."

What about the police investigation – the public appeals, the enquiries, the clues of the early days and weeks? Steve wrote to the police invoking the Freedom of Information Act, asking for access to his files. The reply was an unexpected blow: the notes from the investigation had been destroyed. "And why?" asks Sammy, in a rare flash of anger on her partner's behalf. "If it was a murder inquiry and it was unsolved, they would never have destroyed the files. What gave them the right to chuck all that away?" The police files would have been invaluable to Steve: he can only shake his head in disbelief. In particular, the notes would have illuminated a lead he is keen to follow up – two days after he was found, a phone call was made to Gatwick police by a girl or young-sounding woman who claimed to be his mother. In the cuttings, the caller is reported as having said she was too young to have a baby, and that if her father found out he would kill her. She said the child's name was Michael, and she gave the name and phone number of a woman in Hounslow who would look after him.

According to the press reports, police traced and interviewed the woman but dismissed her from their inquiries. Steve would like to know more, but all details are destroyed. Perhaps, he muses, this was the person who cared for him for the first 10 days of his life. Someone, somewhere, must know something: even if (as the young caller also said), Steve was born secretly, at home, he must have been seen by someone in his first week and a half of life. "I'd like to ask people to think back to early April 1986 – especially people who lived round Gatwick, and maybe round Hounslow," he says. "Do you remember a baby being around and then suddenly disappearing?"

Late last year, Steve wrote an open letter to his mother that was printed in a tabloid newspaper. It attracted messages from hundreds of well-wishers, but little in the way of hard leads. "The only thing we did get," says Keith Collins, Sammy's father, "was a call from someone who said there were a lot of Travellers around the Crawley area at the time Steve was found." It's not a lot to go on, although it might mean that Steve can go back to Dr Wilson in Edinburgh, and ask him to run his DNA sample through a new database he has of Travellers' gene types.

Other leads are even more hazy, like the grainy CCTV footage of a man and woman seen carrying a bundle that might have been Steve into the airport an hour before he was discovered. The newspaper report describes them as a woman in her 20s, and a man who might have been slightly older, both slim with dark hair, and both wearing blue jeans. Despite several appeals for them to come forward so they could be ruled out of the investigation, they never did – but as with the paperwork, the images have been destroyed.

What, though, of the simplest way of answering Steve's questions? Is there a way he could persuade his mother to get in touch? "Of course I realise that she's gone to a lot of trouble to stay hidden, both at the time and over the years," he says. "But times change, and circumstances change. It could be that, while she couldn't acknowledge me in the past, she can now – or in the future.

"I want her to know that I'm not angry with her and there will be no publicity if she comes forward. But there are so many things I'd like to ask her, and so much I'd like to know about my background, and Alanna's. And it's not just a mother I'm hoping to find – it's an extended family as well. I might have siblings, cousins, aunts and uncles, even grandparents."

One intriguing possibility is that, with genetic advances all the time, and with the likelihood that more and more people will have their DNA mapped in the decades ahead, Steve's genes will eventually tie up with someone's, somewhere, on a database, and he'll find someone he is related to. That trail could take him, eventually, to the mother who has hidden her tracks so well and for so long.

Steve acknowledges that even if his search is eventually successful, he knows it won't necessarily have a happy ending. But his eyes are bright and hopeful.

Gatwick Baby: Abandoned at Birth, is on 13 April on BBC3 at 9pm, as part of its Bringing up Britain season. If you have any information that could help Steve Hydes in his search, please email garygatwick1986@hotmail.co.uk