Danny Rogers is a likeable, talented, and highly versatile performer… but there's a moment in this touching solo show when he's upstaged by a dustbin. Not just any bin, mind you, but Dusty Bin – the motorized robot mascot of 1980's quiz show 3-2-1. If you're a certain age, the nostalgia of seeing Dusty trundle onto the stage may be the hook that draws you in; but it's the candour of Danny's bittersweet life story which you'll remember at the end.

As host of 3-2-1, Danny's father Ted Rogers was watched by 15 million people a week – an audience size which contemporary TV-makers can only dream of. And before that, he was a hugely successful variety performer, appearing for royalty and singing with Bing Crosby. Yet he died almost penniless, losing his business and his fortune in the recession of the early 90's; and what happened next is cruel and heartbreaking, made all the more poignant because we see this true story through the eyes of his young son.

The script, created by Danny and writer Tom Glover, is defined by such emotional highs and lows. Danny's narrative follows the history of variety performance as it moves off the stage and onto TV, only to be steamrolled by the fashion for talent shows. There are personal details too, about chasing and achieving a dream – and what it's like when the world thinks you're living a dream, but in truth the good times are over. And of course, there are the universal themes as well: love for a parent, respect for great talent, the urge to feel closer to those you have lost.

Danny tells his story with courageous directness, but it's punctuated by frequent demonstrations of his own formidable skill. He starts with a fiendishly complex patter song, and progresses on to a series of fine impersonations; he can sing, he can dance, and all in all he's a consummate variety performer. I won't presume to tell him that his dad would be proud, but there's plenty here that he should be proud of. And the routines slot seamlessly into the story, offering a well-balanced counterpoint to the straightforward honesty of the narrative; the show as a whole is joyful to watch, despite the sometimes-painful history.

Bin and Gone is impeccably performed – and even more than that, it's beautifully pitched. The highs are exhilarating, the lows are harrowing, but the tension's always broken by a corny joke at exactly the right time. Yes, we get to take a selfie with Dusty, and to play an entertaining round of 3-2-1. But I know now that Ted Rogers was far more than a quiz host – and that this show is about far more than a dustbin.