On a crisp morning on the banks of the Thames, Matt Smith is admiring the sight of a two-man rowing boat, moving rhythmically upstream towards him.

“Not bad, lads, not bad,” he shouts out, as the muscular pair glide past him, their oars barely making a splash as they slice into the water.

“That’s the Olympic double-sculls pair,” he says, with an admiring nod. “Look at them go. It’s all about the weight-to-power ratio, you know.”

Six weeks ago, Smith wouldn’t have known one end of a rowing boat from another, let alone the importance of the weight-to-power ratio. Today, however, it’s a different story. In his latest departure from the universe of Doctor Who, Smith has spent much of the past week on - and occasionally in - these cold and choppy waters a short scull from the spiritual home of British rowing, Henley-on-Thames.

He is filming Bert & Dickie, one of the BBC’s main dramatic offerings in the run-up to this summer’s Olympics. Written by William Ivory, the drama tells of two of the unlikeliest heroes of London’s last Games in 1948 - Bert Bushnell, played by Smith, and Dickie Burnell, portrayed by Sam Hoare.

The odd-couple story has echoes of some of Ivory’s best class-conflicted dramas, Common as Muck and Made in Dagenham. Bushnell and Burnell lived within miles of each other but grew up on very different sides of the tracks, or should that be river. While Bushnell was the son of a boatyard worker from the town of Wargrave, in Berkshire, Burnell was, like his father before him, an Old Etonian, an Oxford Blue and a member of the exclusive Leander rowing club in Henley. He was also, at 6ft 4 and 14-and-a-half stone, considerably larger than 5ft 10 Bushnell, who was ten-and-a-half-stone wringing wet.

The pair epitomised the “make do and mend” nature of the Austerity Games, held amid the rubble and rationing in the wake of the Second World War. Bushnell was one of the leading single scullers of his day and dreamt of rowing alone in the Olympics. But the head of the British rowing team, Jack Beresford, had other ideas and, months before the Games, stuck him in a double scull with Burnell.

“They didn’t see eye to eye on a lot of things outside of training,” says Smith, easing into a foldup chair on the banks of the river as the film crew position the boats for another scene a few yards away. “Our story explores their relationship and the fact that they didn’t get on. But in rowing terms they formed quite a formidable partnership. That’s one of the interesting things about the film, with the context of the war and the aftermath. The fact that those Games went on at all was a bit of a miracle. There was this sort of camaraderie then - couldn’t we do with a bit of that now!”

The film climaxes with the pair’s race against the Danish favourites for the double sculls. Without giving the game away, you’d best be armed with a box of tissues as they row for Chariots of Fire style glory. “Even reading the script, I found myself cheering them on,” Smith smiles.

It is the second consecutive role in which he has played a real-life character, following last year’s portrayal of the author Christopher Isherwood in BBC2’s acclaimed Christopher and His Kind. It was a very different challenge, he explains. “With Christopher there was a lot more film footage to get into. You could explore him vocally and try to articulate and give a version of him. You could try to give him a presence in a much more detailed way.” Smith also travelled to California to meet and talk with Don Bachardy, Isherwood’s lover.

When it came to playing Bushnell, he did not strive for an impersonation. The oarsman died at the age of 88 in 2010, and is survived by his three daughters. His family and that of Burnell have supported the drama, but there was little newsreel footage of him, or even radio interviews. “I’ve had to use more artistic licence,” says Smith. He sees Bushnell as someone with an axe to grind, a working-class hero with an oar in his hand. “Without causing offence to people who are close to him, the story goes that Bert was chippy. But my grandad, my dad’s dad, was a bit like that. He’d been in the war and he was a bit chippy, too. I think there was a sort of toughness to people in England at that time but I think that was because you had to be. There was no nonsense,” he says.

Given how little he knew of the real Bushnell, it was all the more important that Smith understand the sport that dominated his young life. Along with his co-star, Sam Hoare, Smith spent six weeks being taught the basics of boatmanship by members of the Leander rowing club in Henley-on-Thames, including members of the Olympic team training for the upcoming Games.

It was a voyage of discovery. “I had never been in a boat before and there wasn’t much time to prepare,” he says. “So it was a daunting but also exciting challenge. We d get up about seven-ish and train as they were doing.”

A part from the effort of training, Smith found that the biggest shock to his system was the huge amount of food the Olympic rowers eat. “They burn off three or four thousand calories a day, so they eat enormous breakfasts of porridge and fry-ups, then go back for a mega lunch after that. I didn’t eat as much as them, but I still ate way more than I would normally because I was burning it all off,” he says.

Manoeuvring their custom-built boat around the temperamental waters of the Thames was tricky, he admits. “It’s a law unto itself. I didn’t appreciate how difficult it was to stay steady and level. We’ve had our duckings,” he grimaces.

As a teenager, Smith was a talented 400m runner and a useful footballer, before his sporting career was cut short. “The thing that worried me was my back. I had a very bad injury playing football as a kid so I was quite concerned,” he says. “But in a weird way rowing actually was good for my back. You are using your arms and legs as a pulley, not your back.”

His spine may have stood up to the test, but he admits the rest of his body took a beating. “Look at my hands, look at my legs,” he says, displaying his war wounds. “I’ve got blisters on the hand, cuts and bruises everywhere. Calluses. Your bum is the worst thing because those old wooden seats are pretty grim,” he smiles. “It is like everything, it is the tiny details. I loved it, although it s taken its toll physically.”

His injuries, however, haven’t stopped Smith regretting the fact that he can’t play in the football kick-around the cast and crew organise during filming of Doctor Who in Cardiff. “I’d love to play football now. Everyone at work plays on Tuesdays, but they won’t let me. I guess it’s the insurance companies and, realistically, if I turn my ankle over and we can’t shoot, then we’re screwed, aren’t we? You just can’t. It’s a small price to pay,” he says, a little ruefully.

Smith’s admiration for those who row at the Olympics has been raised to an even higher level as a result of his brief stint on the river. “If you look on YouTube at those races with Pinsent, Redgrave, all those guys, you see the physical agony they’re in at the end. It’s like they’ve been hit over the head with a baseball bat. Every ounce of your body, every group of muscles is used somewhere. It’s incredible what they do.”

The experience of portraying an Olympian reinforced something he has felt ever since he broke into acting. “One of the things about playing a sportsman and learning about the psychology and mentality of sport is that there are so many parallels between that world and the world that I inhabit. You see how much you can borrow from a sporting way of thinking,” he says. “There’s practice, for one thing, and that sense of discipline and preparation. Having played a lot of sport, that is something I do instinctively in acting. I’m quite thorough, and I work hard. But it’s also about sacrifice. To be a top sportsman you have to really make a sacrifice about the way you lead your life. And that’s sort of true of acting as well.”

“If you want to give it a good go, you’ve got to make some sacrifices and be as dedicated as you can be. Particularly with Doctor Who; it’s two or three hours of line-learning a night.”

“There are other things, too. Rhythm and balance are extremely important. If you look at the greatest footballers - Zidane, for instance; he has got perfect balance; he’s like a poet; it’s like watching a ballerina; he’s incredible - that also applies to acting,” he nods.

In the background, the cameras are ready to roll once more and the assistant directors are summoning Smith back to the Thames.

“So yes: discipline, practice, rhythm, balance, flair, courage - they are all totally in there,” he says, heading back to his boat in the hope that those qualities will help him stay dry for the rest of the day...

Bert and Dickie is on BBC1 tonight at 8:30pm