TV critics don’t come much more powerful than this: Michelle Obama loves Downton Abbey. In fact, the First Lady is such a huge fan that her staff have apparently been begging ITV for advance copies of the third series, which does not go out in the US until next month. Her husband is also reportedly a massive aficionado of Julian Fellowes’ period drama.

For all that, the actor Hugh Bonneville was astounded when the presidential passion for the programme translated into an invitation to dinner at the White House in March. “It was rather strange – in a good way!” smiles the actor best known for playing Lord Grantham in the hit costume drama.

“To go to the White House is a once-in-a-lifetime opportunity. In fact, the building is not that big. It’s just a modest 20-up, 20-down!

“But it was a really special day, and I felt very welcomed. At moments like that, you do think, ‘My goodness me, this show that was very hard to make in a soggy field near Newbury has been grasped to people’s bosom in so many countries’. You do have to pinch yourself.”

For his latest project, Bonneville finds himself in rather less elevated surroundings. In Mr Stink, which goes out on BBC1 on Sunday, the actor gets down and dirty as the titular tramp who is more likely to be found in the workhouse than the White House.

In this charming adaptation of David Walliams’ bestselling children’s novel, the big BBC family drama this Christmas, Mr Stink is a pongy hobo who has chosen to cut himself off from mainstream society.

However, he is gradually reintegrated after he is befriended on his park bench by a young girl called Chloe (Nell Tiger Free). Taking pity on a fellow outsider, she invites him to live secretly in her family’s garden shed.

We are on the set of Mr Stink, which has been adapted for the screen by Walliams and Simon Nye (Men Behaving Badly). The location suggests that there is a corner of west Ruislip that is forever Lapland. For the climactic scenes of the drama, a close in this west London suburb has been transformed into a winter wonderland, complete with full snow covering, inflatable snowmen and dancing neon Santas.

Bonneville is the opposite of Mr Stink. Where the tramp is curmudgeonly and crotchety, the actor is warm and witty. He also does a very nice line in self-deprecating humour. At one point he grins and says that, “Frankly, all the parts I play are the same performance, just different outfits!”

Later, Bonneville jokes that, “If people say this drama is not as good as the book, you can absolutely blame the author as he has done the adaptation himself!”

He goes on to reflect on the fact that many high up people in the Obama administration are enormous fans of Homeland. “Are the figures turning the wheels of power in the US sending out to their local shop for the next boxset, rather than sorting out their Middle East policy?”

Today, the actor is dressed as his whiffy character – in a huge tramp’s coat tied up with string and a matted beard and hairdo, which looks thick and tangled enough for birds to nest in – and advises me not come too close.

Pointing to his filthy feet, Bonneville laughs and says that, “The full dirty, snot-encrusted make-up takes one and three-quarter hours to complete. They’re very thorough about it. When I finish filming, I get back home and think, ‘What is the point of taking it off? I have got to put it on again in a minute!'”

The actor says he was drawn to this enchanting, if malodorous fairytale because, “It has a Roald Dahlesque relish of stinks that all boys can enjoy well into their fifties. But it also has a deeply touching heart. It’s a story that young people can enjoy with a very simple message: be nice to people less fortunate than yourself.”

Bonneville thinks that Mr Stink also scores because, “It gives great credibility to young people. Young people are so often dissed by the media. David has this wonderful childlike – not to say infantile! – attitude. In this book, he is presenting a child’s view of the world.

He realises they get a bad press and wants to change that. “Mr Stink’s relationship with Chloe is very touching. Like him, she feels an outsider in life because she is bullied at school. She is Every Girl. Everyone at some point in their lives feels excluded and misunderstood. But she and Mr Stink find a kinship. She’s far more active at reaching out and making a connection, and that gives him hope about young people.”

Previously, Mr Stink’s strongest relationship had been with his dog, the Duchess, who in the drama is played by Pudsey, better known as the winner of this year’s Britain’s Got Talent competition. Bonneville says that, “Having spent the last three years acting with a labrador on Downton Abbey, I’m used to the dog being the biggest star of the show. Pudsey is in fact the biggest star in Britain – he’s even bigger than David.”

Hitting his comic strike, Bonneville continues: “Talk about Hollywood behaviour! I’m not allowed to look him in the eye before noon and I have to call him ‘Mr Pudsey’. He has so many engagements, but he deigns to visit us for a few hours every now and again.

“I thought Julia Roberts had a big trailer on Notting Hill, until I saw Pudsey’s. Apparently, he goes out carousing quite a lot with Uggie from The Artist. I gather there was some kind of incident outside the Groucho Club the other night. It was pawi-cuffs at dawn.”

After studying at Corpus Christi College, Cambridge, and the Webber Douglas Academy of Dramatic Art in London, Bonneville enjoyed a steady career at the National Theatre and Royal Shakespeare Company. He went on to be a strong, reassuring presence in such works as the aforementioned Notting Hill, Iris, Lost in Austen, Love Again, Daniel Deronda, Mansfield Park, Armadillo and Take a Girl Like You.

However, the 49-year-old actor was catapulted into another league two years ago when he was cast as Lord Grantham in Downton Abbey. You would imagine the global popularity of that show has given Bonneville extra leverage in the business.

But the actor, who has been married for the past 14 years to Lulu Williams, a full-time mother, and has a teenage son, is typically modest about his new-found industry influence. “I’m asked to attach myself to more projects than I was a few years ago, and that’s lovely.

“But it would also be lovely if any of them got off the ground. It’s one thing being attached to something, it’s quite another hearing the words, ‘Turn over’. I’ve got more attachments than a bulk email – ‘Can’t open attachment. Please resend!'”

The other role for which Bonneville has won praise is as Ian Fletcher, the gloriously incompetent, jargon-spouting head of the Olympic Deliverance Commission in John Morton’s BBC2 “mockumentary”, Twenty Twelve.

The actor will disappoint millions by revealing that there is little chance of the show returning. “The clue’s in the title. They’re great characters, but John feels, ‘How could you raise the stakes to the same degree again?'”

That does not stop Bonneville speculating about an imaginary future for the characters, though. “The show does for management-speak what The Thick of It does for politics. So I wondered about them running the UN and trying to sort out some international conflict or the IMF. Wouldn’t that be hideous beyond belief?”

The actor will also be starring in the seasonal special of Downton Abbey on Christmas Day, in which Lord Grantham takes his family on a summer break to a Scottish castle. Bonneville is just recovering from the storm of criticism his character received for ignoring medical advice and thereby contributing to the death of his beloved daughter Sybil (Jessica Brown Findlay.)

Bonneville says that, “People on Twitter were devastated. I’ve had hate mail and bomb threats, because I’m obviously the most evil person on the planet for favouring one piece of medical advice over another. In some people’s eyes, it’s my fault, because obviously I do live in Downton Abbey!

“I don’t want you to take this the wrong way, but it’s lovely that people are devastated about Sybil’s death. It shows they’ve invested in the world, and it’s a real compliment that they care so much.” According to Bonneville, the demise of Sybil also underlined the strength of the series. “The great skill of Julian’s writing is that he gives all the characters great depths and surprises viewers all the time.”

So what does the future hold for Downton Abbey? Bonneville thinks that, “It’s got a finite life, which is as long as Julian wants to keep writing it. It’s so much his voice. We’ve all agreed to keep doing it as long as his hand’s on the tiller. But it has to finish some time, or else we’ll end up doing doddery old person acting – which some people would say I do already!”

But that’s the future. For the time being, Bonneville simply wants to focus on Mr Stink because, “It’s the perfect Christmas film. It’s a wonderfully feel-good, smell-bad drama.”