The polished alexandrines of Jean Racine’s Andromaque were heard as their writer intended – with surtitles ensuring comprehension – when a compelling production of the play, under director Declan Donnellan, visited the Oxford Playhouse in March. At the National Theatre, by contrast, Nicholas Hytner opts for a translation – a freer, emphatically non-rhyming one from Ted Hughes, first heard shortly after his death 11 years ago – in presenting the tragedian’s last, and many think greatest, work Phèdre on the Lytteleton stage.

The effect is every bit as shattering, perhaps even more so, with the famous blunt forcefulness of Hughes’s poetry adding a new dimension to the horror of what is being depicted. Robbed of their courtly patina, the words suggest in their gutteral urgency a style closer to that of Euripedes, whose Hippolytus covers similar dramatic ground to Phèdre, than that of 17th-century France. Adam Cork’s discomforting sound score of menacing rumbles and half-heard lamentations plays its part in this, as does Bob Cowley’s atmospheric design,with its presentation of a sun-baked palace on a Mediterranean sea shore beneath an azure sky. It had to be admitted, though, that the northern-accented, downmarket delivery encouraged from some of the actors makes it initially difficult to accept that these are events befalling people at the very peak of Grecian society, many of whom are descended from gods.

The focus is Phèdre, magnificently portrayed, with all the intelligence and subtlety for which her acting is recognised, by Helen Mirren. That this is her first stage appearance in six years makes the production a hot ticket. Untouchably hot, perhaps, but seize a ticket if you can; you are unlikely to see finer stagecraft this year.

Phèdre’s predicament is easily summarised: in the absence of her husband King Theseus (Stanley Townsend) she has fallen desperately in love, though she dare not admit it, with his son Hippolytus (Dominic Cooper). When it seems that her husband has been killed on his travels, she is persuaded by her interfering old nurse Oenone (Margaret Tyzack) that it is now safe to reveal her passion for the proudly chaste young man. She does so, to his utter disgust, expressed in graphic terms when Cooper submerges his head beneath a drinking fountain to wash away the vileness of her proposal.

Theseus, though, is not dead and he returns to hear a mendacious account of what has occurred between his wife and son. There follows his ill-judged calling-in of a favour from Neptune, which leads ineluctably to disaster.

A key element to the tragedy, beautifully caught in Dame Helen’s performance, is Phèdre’s recognition of her own blame in the matter. She certainly sees, too, the indignity of her position, even as she is powerless to alter it. Wallowing in her troubles, as she admits she is, she appears to find it almost comical when they suddenly get much worse as she discovers the virtuous Hippolytus actually has a lover, Aricia (Ruth Negga), for her to be jealous about.

“All I have suffered before this,” she grimly states in one of the great passages of Hughes’s script – “The terror, the delirium,/ The agonies of craving, the impossible pain/ Of that brutal rebuff, the horror of my guilt,/ The bottomless degradation,/ The loathing of myself, the despair – / All that was no more than the overture/ For what is taking hold of me now.”

Can you imagine – it is perhaps not hard – the emotion Dame Helen packs into those words? Or the surprise of finding a sudden eruption of laughter from the audience on that necessarily stressed word ‘overture’? It truly is a surprise, but when you think about it, the laughter expresses no more than understandable relief from the near-impossible tension being experienced by the audience.

Phèdre plays until August 27. Booking: tel. 020 7452 300 (www.nationaltheatre.org.uk).