It's historically documented that Shakespeare's daughter Susanna Hall was accused of adultery by a neighbour in Stratford-upon-Avon towards the end of the playwright's life. It's also recorded in church court papers that she won her claim for slander against her accuser, clearing both her name and her reputation.

But a more recent playwright, Peter Whelan, took this bald record of events and crafted a domestic drama of intrigue and suspicion when he created The Herbal Bed for the Royal Shakespeare Company 20 years ago. Now, less than two years after Whelan's death, Royal & Derngate has teamed up with English Touring Theatre and the Rose Theatre Kingston, to revive the play for a nationwide expedition.

In the hands of Royal & Derngate's artistic director James Dacre, it's handsome, beautifully realised and impeccably presented. Dacre's attention to every detail – from Jonathan Fensom's wonderfully evocative set and Malcolm Rippeth's stunning lighting to the unobtrusive underscore of Valgeir Sigurdsson's pitch-perfect music – pays off superbly with a production that challenges assumptions and delivers its history with a healthy dose of scepticism.

There is a conundrum at the heart of the play, however. Whelan's attempt to highlight the problem of moral certainty in an increasingly uncertain world forces him to portray Susanna Hall as a liar and a perjurer – something it's impossible to know for sure at this distance. As a result, the reputation that was restored to her by the ecclesiastical court in 1613 is once more under threat, more than 400 years after the events that Whelan presents.

But let's not quibble over the liberties a playwright may take with the facts for dramatic effect. Because behind any unease about a slandered woman unable to defend her reputation, there's unequivocal admiration for a cast that never puts a foot wrong, offering a performance of classy, assured authority.

Emma Lowndes is a flawed heroine, respectful of her older husband Dr Hall but not in love with him. Lowndes deftly highlights the vacillation between desire and duty, and Philip Correia shares the plaudits with a carefully judged performance as the object of her longings, the draper Rafe Smith.

Jonathan Guy Lewis does ‘tormented husband' perfectly, clearly suspecting the truth of his wife's affections but desperate not to believe it, while Charlotte Wakefield makes a fully rounded character out of the conflicted servant Hester, wanting to please her mistress but wrangling with her own conscience in the process.

There's excellent support, too, from Matt Whitchurch as the boyishly naïve accuser Jack Lane, and an austerely mesmerising turn from Michael Mears as the church inquisitor who threatens to bring the whole deception crashing down. As an ensemble, they work terrifically.

There's more than a hint of Arthur Miller's The Crucible about Whelan's play, with its Puritan overtones and climactic court scene, and Dacre's revival sensibly mines every opportunity for drama from the wordy, thoughtful text. The result is an important production with much to say about personal privacy and morals, and much to enjoy in its lush theatricality.

The Herbal Bed runs at Royal & Derngate until 27 February before touring.