Remember Broadway Danny Rose? He was the hero of, and gave the title to, one of - if not the - greatest Woody Allen films. Danny was the New York showbiz promoter with a talent for signing failing novelty acts that kept him in the tenth division of showbiz, until one day a real talent came along.

He has an East End and -who knows? - possibly even Jewish equivalent in this modern classic (1979) by the late Brian Friel, aka Ireland's Chekhov. His name is Teddy, a Cockney agent whose talented artists included a female pigeon impressionist whose call to her winged assistants would result in her flock descending from the flies and joining her on the stage. It was a nice little earner for Teddy until "galloping shingles" killed the birds – a tragedy from which the act never recovered. Then there was Frank the faith healer, a one man show that Teddy toured in isolated villages and dreary towns all over Britain, accompanied by Frank's devoted but neglected wife Grace.

Usually described as a memory play, Faith Healer is perhaps better seen as testimonial piece. Frank, Teddy and Grace each have their moment of monologue and each of their accounts differs subtly and crucially in fact.

Stephen Dillane's Frank is probably the least reliable. Even his description of Grace turns out to be untrue. She's not from the North West of England, she's Irish just like Frank who, instead of acknowledging their marriage, describes Grace as his mistress, albeit one who resisted asking to be his wife and had the sense to keep a certain distance when she detected his need to be alone. "Her instincts were wiser than her impulses," is the closest Frank gets to complimenting her with typical Friel eloquence.

What all three can agree on however is that every now and then, and in-between all of Frank's many failures, there were moments of inexplicable and astounding success. There was that night in Wales when the crippling conditions of ten hopefuls were cured, and the time when, during a typically fallow period for the act, Teddy took Frank back to the mother country where he made a partially amputated finger whole, but failed to heal a wheelchair-bound boy whose friends then took their revenge.

In Lyndsey Turner's shadowy production, all these gripping accounts of past events taking place in an unspecified period of dreary post-war Britain are told in a mystical but not religious atmosphere. Between monologues, designer Es Devlin shrouds the stage on three sides in curtains of real rain.

As the wry, somewhat world-weary Frank, the bearded Dillane, dressed in a black suit like a lapsed preacher, manages to be both unreliable and completely convincing. Ron Cook as the mouthy Teddy is also excellent as the hard-nosed but romantic showman who never made it big with Frank, but was seduced by mysterious truth of his talent. Meanwhile, Gina McKee as Grace also turns in a beautifully judged performance, transmitting the loneliness and loss felt by Frank's absence, the reason for which Friel's play inexorably reveals like a receding tide.