Bette and Joan, Arts Theatre

Don't go expecting the "But ya are, Blaaanche, ya are" Gothic of Whatever Happened to Baby Jane?. After all, crazy Bette Davis and even phoney Joan Crawford must have been human behind the sacred-monster facade. Anton Burge's new play tries to show us just that in a two-hander set during one day of rehearsals for Robert Aldrich's shlocky B-movie in 1962.

The premise that while Crawford tried to project one-dimensional film-star niceness, Davis was a practical actress who kept it relatively real gives Greta Scacchi as Baby Jane's creator one hell of a part. Would you be surprised to learn that she's note-perfect? I was.

The balance is uneven, of course, and no doubt it's meant to be: Anita Dobson's Crawford talks genteelly of herself in the third person, signs off acid phone calls with sanctimonious "bless you"s and mooches around Davis with a look suggesting the Offended Royal Family, while Scacchi's Bette doesn't give a damn, swears like a trooper and gets most of the best lines (drawn in part rather over-extensively from interview bon mots). Their different takes on the same situation are amusingly counterpointed before they come together for a lower-level action reply of the flamboyantly vile, deranged Jane and the sweetly suffering, wheelchair-bound Blanche in the film they're working on. Bill Alexander's production keeps it simple, along with Ruari Murchison's designs where the only concession to fantasy in the unfussy dressing rooms is a gap in the middle of the mirror lights through which the two women peer without seeing each other.

There's a problem in that neither is allowed to forget she's soliloquising in front of the audience, obliged to catalogue the ups and downs of overlapping careers, shared lovers and failed marriages. By restricting it to a double act, Burge excludes the possibility of the kind of reality available in two other recent London productions about putting on a show, Peter Quilter's End of the Rainbow, where Hilton McRae plays the laconic voice of reason as pianist to Tracie Bennett's Judy Garland, and Jack Rosenthal's Smash!, in which Carrie Quinlan nearly stole the show as inquisitive hotel room service.

What might have made this a more shapely drama is the possibility that Joan and Bette, despite their different backgrounds, could have come closer as sisters under the skin. But that chance goes almost for nothing in Act II as Davis reflects on her one true love, the director William Wyler, while Crawford touches on the family nastiness which made her seek refuge in a prettier world. And here the two actresses part company: while Scacchi's captivatingly well-modulated gamut allows her to scale it down and muse without ever becoming sentimental, Dobson still seems to be playing a role. Even the sudden slashes of viciousness don't have the impact they might; this is a sharp-edged film star without the evident core of steel that would have seen Crawford through, for all the laugh-raising fixed smiles and florid hand gestures. Again, the fact that the unwilling co-stars didn't really go for each other's jugulars leaves the play without any screamingly funny climax: a weighty steel belt and the shipping in of a Coca-Cola machine to punish Crawford as widow of a Pepsi king are no substitute for the dead rats and canaries served up as luncheon for the disabled Blanche in the movie.

But Scacchi does compel, not least because from the start, yes, she IS Bette Davis down to the poached-egg eyes and the well-articulated yoking of olde England consonants to New England vowels. The command never falters, reaching its peak when she finally dons the Baby Jane wig we're all waiting for her to take up (pictured above right) - a high-water mark which is sustained through the opening tirade of Act II, where our actress gets a fright seeing herself in the mirror. And I never thought I'd say this, but now I want to see her play the grande dames of classic theatre: bring on Scacchi as The Cherry Orchard's Madame Ranevskaya. In the meantime, if there should ever be a more meatily written cinematic All About Bette, Greta's undoubtedly your woman.

• Book tickets for Bette and Joan at the Arts Theatre until 25 June
• Find Whatever Happened to Baby Jane? on Amazon

Luncheon served by Bette Davis's Jane to Joan Crawford's Blanche in Whatever Happened to Baby Jane?