In his harrowing 2002 drama The Magdalene Sisters, Peter Mullan exposed the de facto prisons for "fallen" women in Ireland, run in ungodly fashion by nuns up to the 1960s.

Philomena considers a similar phenomenon, but has a softer, heart-warming hue. That is the great art of storytelling, which can offer one perspective that will leave you beaten and bowed, another creating the strongest urge to take your mum for tea.

The different, more feel-good tone to Stephen Frears's film derives largely from its source. Philomena was a teenager when, in 1952, she became pregnant to a boy at a fairground and was despatched by her shamed family to the harsh care of the Sisters of the Sacred Heart. She gave birth in the convent, in whose laundries she was then forced to work. Four years later, the nuns sold her son to an American couple looking to adopt.

Philomena was still searching for him 50 years later. As played by Judi Dench, this seventysomething woman is one of the purest, most indomitable and endearing characters you could ever expect to encounter; a stirring example of how adversity need not affect a person's humanity one jot.

Surprisingly, the film is the pet project of comedian Steve Coogan, whose Alan Partridge: Alpha Papa was released in the summer. Coogan's interest was piqued by Martin Sixsmith's book The Lost Child Of Philomena Lee. While Sixsmith focused on Philomena, Coogan and co-adaptor Jeff Pope bring the writer himself into the frame, charting Sixsmith and Philomena's shared search for her son. It's a smart move, creating a wonderful chalk-and-cheese character study, as the Oxford-educated Englishman and the retired Irish nurse go on the road.

It starts in London with Sixsmith (played by Coogan) at a low ebb, having controversially lost his job as one of the Blair government's spin doctors and considering a new career as a Russian historian. When Philomena's daughter asks him to consider writing about her mother's predicament, he is at first dismissive, declaring that human interest stories are for "weak-minded, vulnerable, ignorant people". But the former journalist can't ignore a cracker of a yarn.

Their journey takes them from the unco-operative nuns in Ireland to America. The last time we saw Coogan in a road movie, it was alongside Rob Brydon in The Trip, the pair swapping quips and impersonations in a bid to outdo each other for laughs. Here Coogan subdues those instincts, playing Sixsmith as a decent but humdrum man and a bit of a snob, bored senseless as Dench's Philomena gives her chapter by chapter account of the Mills & Boon-ish book she's reading, The Slipper And The Horseshoe. The result is just as hilarious.

It's often said that comedians pine to be tragedians. What's refreshing here is that rather than leave his comedy chops at home, Coogan the writer subtly infuses a very sad story with humour, while as an actor he unselfishly plays the straight man to Dench's main event. And she is remarkable, never playing for sympathy, portraying Philomena as a woman very much of her time and class, artless, daft, but with a moral core; she is utterly familiar to us.

Frears is not one of those directors with a recognisable visual style or narrative approach. His trademark is a certain vigour and humour, and a skill for keeping out of the way of the story. Here, our anger, sadness, horror, compassion and laughter are neither sought nor forced. As a result, it's impossible not to be moved.