Ryan Craig's new play is hysterically funny; it's historically fascinating (as it charts the various waves of immigration and the mutations of xenophobic prejudice in London from 1963 to 1982); and – like Hangmen, Martin McDonagh's recent play about the abolition of the death penalty in England – it situates itself in a heightened, near-cod version of the Sixties so that it can be all the more a Play for Today.

Above all, Craig has written the kind of phenomenal role that you pray that an actress of Sara Kestelman's unflagging calibre will come by at the summit of her career. She excels at characters who have been seared by a terrible past but who don't give an inch of ground by succumbing to a speck of self-promoting sentimentality – characters whose “cruel to be kind’ approach displays a terrible moral authority and entitlement.

She can be as slyly funny as any actress alive. Her last London engagement was at Hampstead in Tony Kushner's The Intelligent Homosexual's Guide to Capitalism and Socialism with a Key to the Scripture, in which she drew the most appreciative laughter of the evening as the protagonist's provokingly serene sister who has covered the ideological and spiritual waterfront – Catholic nun; Maoist; Shining Path follower in Peru; you name it. If one of Saki's cats were to develop the weird ability to miaow its way through an over-stoic version of “I'm Still Here”, the effect would not drive one up the wall with more, erm, feline mischief.

And now all these various strands come to a momentous consummation in Filthy Business. Yetta Solomon pulped rabbit skins in the London Underground when anti-Semitic violence in Eastern Europe drove her to this country as a very young girl, cut adrift by history from her family. Her eventual husband sliced his hands to ribbons every day working in a tram factory but, starting with the offcuts of rubber he brought home, Yetta gradually built up the emporium in Holloway (“If it's made of rubber, we sell it”).

She makes the average tigress look lackadaisical in her fierce determination to keep her cubs together. But it's the 1960s now and the young folk have ideas of their own. When her wholly straight young grandson Mickey (excellent Callum Woodhouse) reveals that “I wanna cut hair... styling and that”, she reacts as though he'd just expressed a holiday preference for Palestine.

“Punch da face” she challenges others, and she would certainly punch yours if you suggested she was an immigrant. If she thinks you are plucky survivor too, she will take you under her wing. But woe betide you if you show the least disloyalty. And the little matter of £70 that has gone missing from the till results in a floating spotlight of possible culpability that raucously severs some of these hard-won connections.

We certainly don't hear the first stirrings of political correctness when Yetta gets going on the estranged Nigerian husband of one of the protegees: “Yah yah, I don't want to hear no sob story shit from you. You want to talk suffering mit me? My people got five t'ousand years of suffering. Beat dat.” She's majestically indifferent to the idea that his country has suffered from the map-making stupidity and broken promises of her adopted British: “Listen, mister I got my own problems”.

She left me feeling as weak with laughter as Dame Edna does. But there is also the chilling sense that she is inching towards the blasphemous binary: the matriarch who, in defence of her values, ends up as isolated and self-authoring as Richard III or Milton's Satan.