The youthful appearance of both actresses and their extraordinary versatility, which means they can still play parts often associated with younger women - Dame Judi was a memorable Cleopatra a few years ago - belies the fact that both actresses are 58, not young in theatrical terms, though still some years off the age when the late Dame Edith Evans became the grand dowager of British theatre.
Maggie Smith, in fact, opens in Wilde's The Importance of Being Earnest at the Aldwych next week, playing the role of Lady Bracknell, which in spite of a portrayal by Judi Dench some years back, is forever associated with Dame Edith's stentorian tones.
The return of Maggie Smith to the West End after a five-year absence is a particular pleasure for theatregoers. Her talent has ranged from revue with Kenneth Williams in the late Fifties to both comic and tragic roles at the National Theatre in its most memorable years in the mid-Sixties, when she played opposite Laurence Olivier in Shakespeare's Othello and Ibsen's The Master Builder.
While making many films from The Prime of Miss Jean Brodie to the recent Lonely Passion of Judith Hearne and doing theatre work in Canada, her appearances on the British stage since the Sixties have not been quite as frequent as her admirers would have hoped.
Dame Judi by contrast, while also doing regular film and television work has, like the third member of her generation's clutch of leading actresses, Vanessa Redgrave, rarely been away from the London stage for any sizeable period. In two weeks Dame Judi stars in the West End opening of the Royal Shakespeare Company's production of Peter Shaffer's The Gift of the Gorgon.
But if nothing acts like a dame nor attracts like a dame, are they soon going to run out of parts, with modern playwrights, like their classical forebears, continuing to fail to write parts which will give scope to our most popular performers? However, performances of both The Importance of Being Earnest and The Gift of the Gorgon are already selling out in advance bookings.
Actresses have traditionally been starved of parts between playing Lady Macbeth and the nurse in Romeo and Juliet. It is one of the reasons that Glenda Jackson left acting for politics. There is no King Lear for women in their Fifties to look forward to. The actress Juliet Stevenson says the dearth of parts, particularly classical parts, for older women is one of her recurring worries, even though she is only in her thirties.
'It's just agonising that actors have a chance to get better and become more interesting, more lived-in, more feisty. It's almost impossible for a woman to start making her career in her mid-forties. They just don't kindle writers' imaginations in middle age. There's only room for a clutch of actresses to maintain their careers in their forties and fifties.'
Nicholas De Jongh, theatre critic of the London Evening Standard and also author of a book about homosexuality in the theatre, says that the popularity of Maggie Smith, in particular, has been enhanced by a gay following: 'She has a wonderful sense of high camp.'
But he says that there have been some parts for older women in the work of such playwrights as Pinter, Osborne and Howard Barker, and expects the popularity of our leading actresses to continue and increase as they approach their sixties.