In March 1960, on the day Elvis Presley passes through town, two people meet by chance at a fog-bound Prestwick Airport. She carries a teddy-bear and a fancy embroidered holdall; he’s wearing an Elvis badge and an army duffel-bag. He’s a nice but unremarkable Yorkshire lad, while she’s a commanding doyen of the stage. But you shouldn’t always go by first impressions – and as they chat, we learn they have more in common than it seems.

The woman is actress Margaret Rutherford, played here by Kellie Gamble as an indomitable cross between a hospital matron and Lady Bracknell. At the time this play is set, Rutherford’s iconic film role as Miss Marple is still ahead of her – but she’s already well-known (and as she regretfully concedes, already thoroughly typecast). She can be a little self-obsessed: after Albert shares a memory of his war-scarred childhood, Rutherford just talks about the West End. But her heart’s in the right place, she’s refreshingly unashamed of everything that makes her, and if some of the dialogue’s blatantly there to brief us on her history, it’s a history well worth learning about.

On the other side of the stage, Ant Hopkinson’s portrayal of Albert is a lesson in restraint. He’s likeable from the start, but plays his cards closer than the talkative Margaret, and we’re a long way into the script before we get any idea of what truly makes him tick. He’s a symbol, perhaps, of generational change: hilariously unmoved by the names that Margaret drops, yet endearingly animated when he talks about Elvis. He says he’s enjoying army life, but we can tell there’s something awry.

This is all fiction, of course, but playwrights Clara Nel Haddon and Ray Globe made a smart choice when they inserted Rutherford into their storyline. She’s halfway between the quotidian Albert and the superstar Elvis; popular enough to enjoy her fame, but wise enough to recognise the gilded cage the King has been locked in. Yet Albert is caught in a trap of his own, a poignant urge to force himself into a shape he was never built to be. By popping the bubble of Elvis-envy, Rutherford makes space for a smaller dream.

Haddon and Globe’s message will be resonant for anyone at the Fringe, and it contains a convincing thesis about the nature of art, artists and artistry. The moral is ultimately simple – the kind of pep-talk we’ve all received at some point in our lives – but this is a quiet and believable story, which doesn’t demand a revelatory conclusion. It’s a parable of meeting the right person at the right time, and the lessons we can learn from those who precede us. And it’s a celebration, too, of the universal hunger to find where you belong, a drive with the power to connect contrasting lives.