It may surprise you to learn what Tom Daley is planning for after the Olympics. A very big party? A long holiday in Florida? No, he’s determined to go back to school, so that he can finish his maths A-level and prepare for his Open University degree in Spanish.

Tom is a rare young man who seems to have bypassed adolescence and gone straight to national treasure status, despite only turning 18 in May. Adored by teenage girls, he claims he’s never finished a drink, and seems truly at ease with his topsy-turvy life. He jokes that he spends most of his time half-naked – “it’s how people recognise me” - and since he was nine, he’s been throwing himself off 10m diving boards 20 times a day, at a speed of 35 miles an hour.

Every year, he travels once around the world between diving competitions (Moscow-Beijing-Mexico-Texas is the usual route), doing his homework on the plane. He has a schedule that leaves me breathless, with training camps, competitions and school all interlocked with military precision. It leaves him with no time for girls. “It is very hard to have a girlfriend at the same time as being a full-time athlete,” he told me. “So I would much rather give my full time and attention to the Olympic Games, as it is such an important year for me.” He is charming, immaculately polite and good fun. The boy, when he’s ready, you’d want your daughter to marry.

I first met Tom one cold morning in January 2010 when there was snow on the ground. He bounded to the door of the family home in Plymouth, grinning and jostling with Rob, his dad; the two of them had just raced back from sledging on Dartmoor. “I saw snow and just wanted to go,” he said. He had 20 minutes before he was due to go to training and spent the time competitively bantering with his dad about the countries he’d fly over en route to the Commonwealth Games in Delhi. Tom is very competitive. He’ll lose graciously in the diving pool, but I’ve seen him furious with himself for not beating his younger brothers in a tie-tying skirmish in the kitchen.

In those early days of filming, Rob – “I’m just an unpaid taxi-driver” - endlessly drove, cheerily, honking his do-dee-do horn and waving at passing cars. These rhythmic regular journeys from home to Plymouth College were to become our favourite memories. This was where Tom and his dad shared their world of spiralling bad jokes and teasing. Tom could poke at his dad’s double chin and neck and exclaim to the camera, “Look, doesn’t this really annoy you?”

I made my first, 2010 film about Tom, The Diver and His Dad, because at 15, Tom was 10m diving world champion and his dad had cancer. He was soon to sit his GCSEs and was sharing a bedroom with his younger brother, Ben. His medals, pinned up in a long line around the ceiling, were starting to keep him awake as they swayed in the air. So Rob and Debbie built Tom a new bedroom above their kitchen.

The room was bare save an enormous 42in TV on the wall. One day we filmed Rob as he assembled the surprise furniture they’d ordered. He spent two hours putting it together a dozen times and then redid the drawers 60 times before he was satisfied. “It has got to be perfect,” Rob kept saying. Debbie remarked that as a three-year-old Tom insisted on his set of toy cars being lined up to face the same way, all absolutely straight. Like father, like son - complete perfectionists.

Now Tom is 18. I’m often asked what he’s like, and it’s easy to answer. He has a direct stare and a very quick brain. He is unfailingly helpful, cheerful, and he makes me and the crew laugh. He can be grumpy, he is not a morning bird and woe betide you if he gets hungry - he needs food and lots of it. Recently he has lost a stone for the Olympics, despite a secret chocolate stash. His bedroom can be messy. He can nag - but only with good intentions. Currently he’s nagging his mum (he calls her Debs) to keep up her running (Debbie ran the London Marathon for the Samantha Dickson Brain Tumour Trust, raising 11,000).

Six months after we finished The Diver and His Dad, we started filming Tom Daley: Diving for Britain, which is broadcast this week on BBC1. Rob had fallen very ill, with a second tumour, in January 2011. “Come down and film again,” Rob had said. He liked filming and he liked most journalists. Since Rob had given up work, he enjoyed their company. He liked the structure of a filming day, which always started for him with a school drop-off, then a quick trip to McDonald’s. For a man whose favourite drink was Coke, he made a mean cup of tea. He was determined to keep going for Tom and the boys. “What will I do if I don’t get to 2012?” he’d reflect.

As it was, Rob never got further than the national championships in Sheffield in April 2011. He arrived in a wheelchair, clutching a Union Jack, amazed he’d made it, and joking about Debbie’s driving. He could barely walk to his seat and tears rolled down his face. He looked stunned - at being there following another brutal round of chemotherapy, and at the knowledge that, after years of following Tom around the world, this could be the last time. Tom won gold in the synchro event with Pete Waterfield, beating the Chinese into second, and Rob sang his heart out to the national anthem. It was a happy day.

Tom flew to Mexico the next day, but a week later Debbie called him to come home. His dad was dying, having survived several scares. For the next few weeks, Rob was nursed in the living room by his family and a rota of nurses. His speech worsened, but he could hear and squeeze your hand. One day Tom texted me, “Come down, bring your camera, we think you should film. I want people to know how difficult it is for him, and for us to lose him.” Late one night Tom broke down. “Cancer is a terrible thing. I know I’m not the only person going through this and other people lose a dad, but I love him so much.”

Now every morning when he wakes up, Tom looks across to two photos of his dad flanking a small, heart-shaped container that holds his ashes. “I touch it every morning and say hello. It used to be really weird thinking my dad is inside that, but now I’m fine with it.”

Overall, Tom has coped well with his father’s death, though I have seen him very upset. He only took one day off from his diving schedule, because he knew his father would have been mad at him if he didn’t continue. For a long time he felt numb and didn’t know what to feel. He carried on training, five hours a day, morning and afternoon, wrapped around lessons.

The past 15 months since losing his dad have seen Tom’s life change dramatically. He’s now the breadwinner and becoming a brand, with sponsorship by BMW, Nestlé and Adidas, and he can drive. Since making the 10m platform final at the Beijing Olympics, he’s big in China, with 1.5 million followers on Chinese Twitter. And with success - the world championship title in Rome, 2009, double gold at the 2010 Commonwealth Games - has come international recognition. He has designed his own website and online TV channel, ghosted his autobiography and been sculpted by Madame Tussauds. But he hasn’t changed. He still bounds to the door and puts smiley faces in texts. He loves making cupcakes and babysitting his cousins. He was boyishly excited when his Team GB kit was delivered. Much to his amusement, the trunks have all been made too big and will have to be changed. He grimaces at the number of days to go. “It’s come round so fast. My heart beats so loud at night I can hear it when I think of competing.” But he also can’t wait. When Tom was seven he drew a picture of himself in the 2012 Olympics, before anyone knew it was to be in London. Now he will sense Rob around him, waving his flag from up above, and he grins widely at the thought.

Tom Daley: Diving for Britain is on tonight at 10.35pm (N Ireland 11.15pm) on BBC1