His parents are haunted by the stark, still-frame closed-circuit television footage of their son leaving King’s Cross. In three consecutive shots, Andrew Gosden walks from the concourse towards the railway station exit and emerges on to the pavement.

Small for his age and slim, he is 14 but looks younger, perhaps 12. He is wearing a black T-shirt and jeans and has a black canvas satchel slung over his shoulder.

He has left behind a secure home, a loving family and a glittering array of school prizes. Ahead is London, that great, sprawling, teeming, terrifying city with all its allure and danger. He looks so young, so vulnerable.

“If we never see him again, that’s going to be the last photograph of my son. That’s what really gets you in the guts,” says Andrew’s father, Kevin.

Every year, an estimated 100,000 under-16s are reported missing. The vast majority return safe and well within 72 hours, according to the charity Missing People.

Some are fleeing abuse, bullying or family conflict. Others seek to escape some “low-grade issue they don’t feel they can talk to their families about”. Sometimes, the children are simply seeking an adventure.

Andrew’s case is unusual not merely for the length of time he has been missing, but also because there seems to be not the slightest clue explaining his decision to leave home.

The bare facts are these. At 8am on Friday, September 14, eight days into a school term, Andrew left home — a neat Victorian terrace in Doncaster, South Yorkshire — in school uniform for his short walk to the bus stop. His sister Charlotte, 16, had already set off.

The night before had been a standard evening at home. The family ate together and Andrew played a jigsaw game with his father on their computer before watching some of his favourite television comedies with his mother, Glenys.

On that Friday morning, however, he had no intention of going to school, where he had a 100 per cent attendance record. Instead, he walked to a park and waited until 8.30am, when he knew that his parents — both speech and language therapists — would have left for work.

Andrew then returned home, let himself in with his key and changed out of his uniform, leaving his blazer neatly hanging from the back of a bedroom chair and placing his shirt and trousers in the washing machine.

In T-shirt, jeans and trainers, he walked to a local garage, withdrew £200 from his savings account at a cash machine and headed for the station, where he bought a one-way ticket to London. The woman who sold him the ticket remembers thinking that he looked quite young. She asked him whether he was sure he wanted a single. Andrew was adamant. A passenger on the 9.35am Doncaster-London train recalled sitting opposite a boy matching Andrew’s description exactly. He sat quietly, playing on his portable PlayStation.

When staff at the McAuley Catholic High School, in Doncaster, realised that he had not arrived they phoned the family at once. Critically, the contact list was misread and the numbers phoned were those of a different pupil.

Mr and Mrs Gosden, therefore, did not realise that anything was amiss until late afternoon, when Andrew — known to the family as Roo — did not come home from school.

His uniform was soon found. Andrew is the sort of boy, his father says, “who leaves you a note if he goes to the shop on the corner”. After a few quick phone calls drew a blank, Mr Gosden contacted the police.

Detective Inspector Martin O’Neill heads a team of officers from the South Yorkshire force who are working on the case and have paid several visits to London in search of Andrew.

They did an immediate risk assessment and put Andrew in the highest category because of his age, his perceived vulnerability and his vanishing act being “totally out of character”.

It took only three days to establish that Andrew had arrived in London at 11.20am on the Friday. It would take another 24 days before the CCTV footage of him leaving King’s Cross was discovered. The police have paid several visits to the school. They have spoken at length with his family and friends. They have no theories that would explain his disappearance.

For five of the past six weeks one or both parents has tramped the streets of London in search of their son. They have put up posters, toured Andrew’s favourite haunts — such as the Science Museum and the Natural History Museum — and questioned many strangers.

Mr and Mrs Gosden have also tried to drum up media interest. They have had some success, but there are a lot of missing children. There have been reported sightings of him in London — at a Pizza Hut in Oxford Street, in a park in Streatham, leaving a local train at Waterloo — and farther afield, from South Wales to Birkenhead. None has been confirmed.

“We’re doing everything we can to find him, but it’s very concerning. Andrew is a very intelligent boy, very gifted academically, but he may not be very streetwise,” Mr O’Neill said.

At McAuley, Paul Gray, the deputy head, said that “a visible cloud” was hanging over everyone who knew Andrew. “He’s a very likeable, self-effacing boy. No one’s got a bad word to say about him. This is not the sort of school where you can get lost in the system. If there had been any bullying going on, we’d know about it.”

Andrew was in the top set of his year group for every subject but his greatest gift is as “a natural mathematician”, winning a host of gold awards in national and European competitions.

Martin Taylor, one of his teachers, said that Andrew would comfortably achieve a first-class honours degree in the subject at Oxford or Cambridge.

“He’s quite a shy lad, but he has a fantastic smile and I’ve never seen him down or sullen,” Mr Taylor said. “Andrew is deep and mature beyond his years. He’s quite self-contained and happy in his own company, but he’s not a loner. He always had a little posse of friends with him.”

Yet something prompted him to head for the bright lights.

Kevin Gosden, 41, and his wife, who is 43, are committed Christians. They have sacrificed a lot for their two children and they would probably admit, in private, that they thought they had done a pretty good job as parents.

Now a family history is being deconstructed. Has there not been enough love, or too much? Have the children been given too little independence, or too much? What have the parents done wrong? They thought that Andrew would talk to them about anything. They were wrong. In their tired eyes is fear for a missing child, but also bewilderment, hurt, a little anger and a shattering sense of rejection.

“You can’t grow up in this house and think that nobody gives a damn about you. He knows how much we love him, so of course it’s hurtful,” Mr Gosden said. “You wonder, what is so wrong with us? What was so wrong with growing up in a supportive family, going to a good school and having a bright future ahead of you? But then you think about Andrew, this boy who has always been so cheerful, who didn’t seem to have any problems and who is the gentlest soul. It just doesn’t make any sense.”

This is a boy to whom everything came easily. Andrew’s sister Charlotte has 11 GCSEs, nine of them graded A*, but said: “I can get the grades, but I have to work hard. He doesn’t have to try. Nothing seemed to bother him.”

Looking in vain for an explanation, the family wonder why Andrew twice chose to break his normal routine, walking home from school instead of making the four-mile journey by bus.

Was he preparing for a future of wandering the streets? And if so, why?

His parents thought initially that he wanted to prove something to himself, or to them, to show that he could stand on his own two feet.

Andrew seemed unusually content to stay at home in the evenings. He never went to a friend’s house or had anyone round, still less hung around on street corners. He was given a mobile phone for his 12th birthday, but rarely used it and did not want to replace it when he lost it.

Could it be that beneath a surface contentment at spending most of his free time at home, Andrew felt stifled and nursed a desire to rebel?

Although the Gosdens are Christian, they encourage their children to make their own choices. Andrew had not been to church for 18 months. His interest in goth clothing and music was not a source of friction.

Mr and Mrs Gosden had suggested that Andrew travel alone to London during the summer holidays to stay with his grandmother. He did not want to go. Had his trip been planned as an awfully big adventure, then surely it would have lasted for a few days at most. If the worst has not happened and he has not fallen in harm’s way, then what sent him to London in the first place may also be keeping him from making contact with home.

Mr and Mrs Gosden are keen to send their son a message: “We love you and we care about you. You have left a huge gap in our lives. We want you back with us but we also want to know that you’re OK. Even if you don’t want to come back, please let us know that you’re OK.”

If you think you have seen a missing person, call Missing People’s 24-hour, confidential Freefone service on 0500 700 700, or e-mail seensomeone@missingpeople.org.uk

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