To read the summary plotline of Kelly Macdonald's new film Puzzle – which tells of a suburban housewife and mother from Bridgeport, Connecticut, who finds meaning in life through the world of competitive jigsaw puzzling – it's possible to imagine the kind of whimsical affair which would make Wes Anderson proud. Yet instead, this remake of the 2010 Argentine film of the same name is a thoughtful realist drama, tied together with a quietly masterful performance from its lead.

'That's interesting,' says Macdonald of the imagined Andersonisms (which I had already dispelled when I saw the film). 'No, it feels very real, and that's what I like about it as well. None of the characters are caricatured. The husband (played by David Denman, who is bear-like onscreen next to the petite Macdonald) isn't a big, brutish, sexist man. He genuinely loves his wife, but he's just very old fashioned in his approach to her. And Agnes, this little woman, she's beginning to change and it has this ripple effect in the family around her.'

The directorial debut proper of producer Marc Turtleaub (whose credits include Little Miss Sunshine and Safety Not Guaranteed; he also directed a version of Marie Phillips' novel Gods Behaving Badly in 2011, although it wasn't generally released), Puzzle pulls off a neat balancing act. It bears a movie-of-the-day accessibility, but blends it with a refreshing abstinence from melodrama and an extremely subtle relevance to today's concerns. Agnes' marriage to mechanic Louie is loving, in a way, but characterised by a duty and subservience brought on by small town tradition where women are concerned. Her chance of a revived life in the big city is instigated by her new puzzling partner Robert (a shabbily cultured Irrfan Khan), summing up the much remarked-upon town-versus-city divide in America.

'It was the usual, you read the script and if you respond to the material you meet with the director,' says Macdonald, speaking at the Caledonian Hotel in Edinburgh, a few hours before Puzzle opened the Edinburgh International Film Festival. She isn't far from home, living once more in Glasgow after time spent in London and New York. 'So Mark came over to London while I was filming Holmes and Watson (her next film, a comedy starring Will Ferrell and John C Reilly) and we had a nice meeting. Agnes' story was just so appealing. She's a very ordinary person, her life has been given over to her family, and she's very much immersed in her role as a mother and wife. But it's that lovely thing where she becomes extraordinary in a sort of quiet, profound way.'

What kind of research did she have to do for the role? 'I didn't ever Google jigsaw competitions,' she says. 'I didn't even do a jigsaw before we started filming. I did work on the accent, I was very concentrated on that, and we had some cast… not really rehearsals, but we talked through some scenes and we all went out and made some Hungarian food together in New York, and drank wine and got to know each other a bit.'

Once again her accent is exceptional, with the crisp, middle class Glaswegian which Macdonald employed in her 1996 debut role in Trainspotting – it's her own accent – and carried with her through the early years of her career having already been cast off to striking effect in the Coens' 2007 No Country For Old Men, a defining career moment. Her American English was further exercised by five years on Boardwalk Empire as Margaret Thompson, wife of Steve Buscemi's Nucky. 'I did West Texan in No Country,' she says. 'I'm good if it's very specific. If I'm told to do a general American accent, mid-Atlantic they call it, I'm f'ckin' screwed, can't do it for love nor money. But if I'm given a specific place I enjoy the process.'

Although in a far less notably flashy production, Agnes' is a strong part which feels just as significant to Macdonald's career as No Country. A prolific and diverse actor, her work until now has consisted of ensemble pieces and strong supporting roles; only the kind-of shared lead with Bill Nighy in David Yates and Richard Curtis' 2005 ecological television drama The Girl in the Café and her lead voice character in Disney/Pixar's Brave (2012) have come as close to illustrating her ability to carry a film.

'Well, I think of everything as an ensemble,' she says. 'I think of this (Puzzle) as an ensemble as well. But I mean, it's Agnes' story, I can see that… I will concede! Yeah, I'm up there onscreen in every scene, it's uncomfortable viewing for me. It was funny because we shot the family scenes first, Agnes and her husband and the kids doing that, then they all wrapped filming and left, and I kind of wanted to go with them. "You're my people, where are you going?" Then Irrfan arrived and we shot all that, and it felt almost like two different films.'

I begin to tell her about the Guardian's review of Puzzle, which I had seen that morning, and which suggested that within the British film industry she might be under-rated… 'I think I'm rated just fine!' she shoots back, with mock indignation. Okay, not under-rated, more under-valued. The key review quote is 'Compare how vital Kelly Macdonald was to 1996's Trainspotting with her cursory presence in 2017's boysy sequel, and you'll have some sense of how the British film industry has underestimated her', which also nails how Danny Boyle's film wasted its most interesting character and performer.

Yet with Puzzle, Macdonald shows a deft and effortlessly commanding ability to lead a film, which is a job she's rarely been trusted with until now. 'Yeah, I realise I've been given an opportunity that I know many other actresses higher up the echelons could have had,' says Macdonald, sidestepping with graceful diplomacy. 'I'm grateful to be given the chance.

'I like to play interesting characters,' she continues, 'and I'm lucky, it's getting more and more interesting. Who would I like to play? I mean, a lot of my choices are about what would make my kids happy, so I would love to do something big and fabulous for them. I'm very grateful for what I do get to do, and I've got a part in Harry Potter (as Helena Ravenclaw in Deathly Hallows Part 2 [2011]), they're very happy with that. But can I get a part in Star Wars, please? That would really impress them.'

Puzzle will go on general release later this summer.