There is sympathy, warmth and directness – though perhaps not much in the way of explicit joy – in this intensely English true story that made headlines and changed lives around the world.

Screenwriter Jack Thorne and director Ben Taylor dramatise the heartache and strain and triumph that led to the first ever birth of what the press with a mixture of hostility and awe called “a test-tube baby” – that is, a baby conceived through in vitro fertilisation – on 25 July 1978: a little girl called Louise Brown (middle name Joy).

It was a medical breakthrough whose decades-long gestation involved dogged but underfunded research, media rancour and personal strain. The resulting drama is watchable, if a little functional, sometimes feeling like an adapted stage play.

James Norton plays pioneering biologist Robert Edwards, a bullish Cambridge scientist impatient with establishment resistance to his ideas; Bill Nighy, with his usual reticent elegance and gentle aplomb, plays obstetrician Dr Patrick Steptoe, whose revolutionary technique could make Edwards’ new ideas a reality – and most importantly of all, Thomasin McKenzie winningly plays embryologist nurse Jean Purdy who was the driving force for the research, which she carried out often while caring for her ailing mother – affectingly played here by Joanna Scanlan – and was the first person to recognise and describe the historic cluster of dividing cells.

In fact, Purdy’s scandalous exclusion from the official record after her heartbreakingly early death from cancer at the age of 39 is a later story the film doesn’t get round to telling. (But the appearance here of DNA scientist James Watson – who led the moral panic against in vitro research – has a historical echo. He and two other men got their Nobel prize, while erstwhile colleague Rosalind Franklin, who also died young from cancer, was for years unremembered.)

Edwards, Steptoe and Purdy emerge from this film as the intellectual odd-throuple of fertility science – and there is a likable, easy onscreen rapport between Norton, Nighy and McKenzie, as the trio plug doggedly away at their work, and commuting between Cambridge, where Edwards and Purdy were based, and Oldham, where Steptoe worked.

The hospital’s operating theatre supervisor Muriel Harris is formidably played by Tanya Moodie as a kind of composite “Matron” figure, blending the real-life person with NHS staff generally.

And what of the forces ranged against them, as they battled to cure the secret agony of infertility? The loathsome, reactionary press – unwilling or unable to grasp that IVF does not carry an increased risk of birth defects – are largely off-camera and they are always being testily dismissed in dialogue scenes, though their long-term effect on the heroine and heroes is not obvious. Edwards gets an (apparently imaginary) TV debate with Watson, and the studio audience are yelping with dismay at the fake news that Watson is doing nothing to suppress. The medical establishment, in the form of the Medical Research Council, shrugs at their work – and Edwards demands to know if they would be more interested if it was a “male” issue: a shrewd point.

As for the religious scruples, Thorne imagines a specifically religious tension between Purdy and her mother, which perhaps creates a certain type of side-melodrama the story didn’t really need. Inevitably, Purdy’s own childlessness is foregrounded and the film has Purdy actually being gynaecologically examined by Bill Nighy’s caring and fatherly Steptoe as a kind of personal-slash-professional favour to her – a rather bizarre moment, arguably, but Nighy and McKenzie carry it off cordially enough.

And so the trio’s story is amiably portrayed, with McKenzie’s Jean bicycling all over picturesque Cambridge, including the courts of King’s College – and in other scenes settling down with Edwards for another motorway caff lunch of egg and chips on the way to or from Oldham. She is the one on whom a personal toll is being taken – the men are relatively unaffected – but even she doesn’t seem terribly worn down. It’s a somewhat stagey reconstruction but an approachable and humane account of a great moment in scientific history.

• Joy screened at the London film festival; it is in UK cinemas from 15 November, and on Netflix from 22 November.