It may have been first performed more than 400 years before Christ. But as the startling, shaven-headed, sharp-suited King Oedipus of Ralph Fiennes at once reminds us, Sophocles’s tragic hero with one hell of a past speaks just as much to us as ancient Greece. Jonathan Kent’s production, with a foot both in camps ancient and modern, still has a terrible fascination about it. Fiennes duly has a big, brave, bold shot at a role that demands the emotional virtuosity of a Gielgud, Scofield or Redgrave and to whose high notes he cannot entirely rise.

True to a hint in the programme, watching Fiennes’s Oedipus, by progressive turns haughty, shifty, elementally aghast and cut to the blinded quick, is to witness a man intent upon being his own psychoanalyst, in remorseless, fearful pursuit of the self he never knew he was. Thanks to his invaluable take upon the character, this Oedipus comes to seem not just a man who has unknowingly killed his father and in ignorance married the woman who bore him. His Oedipus speaks to us about our fear of self-scrutiny and self-discovery, our facing up to discovered truth and somehow bearing it. Jasper Britton’s brisk, affably relaxed Creon offers a suitable, temperamental contrast, though turns scathingly contemptuous when taking over the reins of power.

Kent’s Oedipus makes such a disconcerting, uncertain impact because of its clash of ancient and modern styles. Paul Brown’s stage, with a tilted, revolving disc, is dominated by huge, burnt-copper double doors and appears splendidly ancient. Yet a wooden table with benches attached could have been loaned from the garden of a country pub. There are no observable symptoms of the ghastly plague except for brief views of ruined trees and sinister birds astride them. The Chorus, always a source of anxiety for contemporary directors, is here disastrously rendered by 15 sombre, suited, middle-aged, socially superior gentlemen who variously speak, sing and chant —often drowning out each other’s words. This failure may well be fortunate. For the words they have to speak are more often ridiculous than sublime. Frank McGuinness, an always interesting, individual playwright, is not the best of translators. His new version of Oedipus has been hyperbolically savaged by Germaine Greer, who ignores McGuinness’s gift for terse compression and avoidance of stately archaisms. Even so, far too much of the McGuinness text, particularly his speeches for the chorus, a group akin to dignified but slightly disturbed MP, sounds preposterous. “You can’t leave this for others to clear up,” sounds a typically low-rent note.

A shirt-sleeved Fiennes, collapsing in the arms of Alan Howard’s sombre Teiresias or in the lap of Clare Higgins’s oddly subdued Jocasta, who’s dressed up to look unsuitably common, adopts the hunted look of a man on the run. When finally confronted by the truth he emits a long, muted shriek of pain that chills the blood. He tears open his mouth in a soundless scream of grief. Blinded he resembles a Beckettian vagrant. It is an evening of many flaws, but as Fiennes demonstrates, Oedipus remains irresistibly terrifying.

Until 4 January. Box office: 020 87452 3000, www.nationaltheatre.org.uk