@ Edinburgh Playhouse, until Sat 30 Jan 2016

It’s a fine noise a big band makes but who now remembers Artie Shaw or Tommy and Jimmy Dorsey? It’s Glenn Miller that’s the go-to guy for those swooping, swoon-inducing sounds of the 1940s. Maybe fame relies on the old Jimmy Stewart biopic. Maybe it’s the fact that Miller was tragically lost in action over the English Channel towards the end of the war – he was only 40. No matter, his music remains the soundtrack of the Second World War. In every documentary or movie that wants to paint the 1940s up comes Moonlight Serenade or String of Pearls.

In this amiable touring production of Miller’s life story we get Tommy Steele, a live big band on stage and some ravishing dancing – all this and World War II. Steele is now older (by four decades) than Miller was when his plane disappeared from the radar screens. The nimble Steele – who shot to fame as the UK’s Elvis 60 years ago – celebrates his 80th birthday this year.

Every so often Steele comes out of character to address the audience himself and help advance the story. It suggests that he might have been better employed as narrator rather than playing Miller with a rather patchy American accent. For all that, Steele has great stage presence. We can even forgive the age gap between Steele’s Miller and his missus (the brilliant Sarah Soetaert).

The dance numbers have terrific snap and Glenn Miller’s story is told economically. The set looks like a cross between a giant Nissan hut and the Hollywood Bowl and offers as little distraction as the storyline. The music is fantastically well done, it’s good-hearted, uncomplicated and so cheerfully optimistic that it’s sure to send you out into the night with a beaming smile on your face. It’s provided by a 16-piece orchestra which, like the original, prided itself in its unique brass and saxophone sound. When the seated musicians appear on stage and belt out the hits there is huge emotion in the auditorium – not just for a bygone era but for a hopeful sound which in wartime roused, inspired and cheered. It’s clear why Miller won the first ever gold disc and why his great number Tuxedo Junction sold 100,000 records in one week.

Naturally there is a huge nostalgia trip with Miller’s music but it’s more than that. In the six years of his greatest fame he and his orchestra had a slew of chart hits (yes, they had charts back then). They were wonderful, bighearted, numbers guaranteed to chase the blues away and get people up on the dancefloor. Glenn Miller was the Calvin Harris of his time. And heaven knows with today’s doom and gloom headlines we certainly need a bit of uplifting. The story of the trombonist with a heart of gold and lungs of steel (pun intended), his marriage and rise to fame is told with relish. Director Bob Tomson injects huge energy into proceedings while Tommy Steele captures Miller’s charm-boy ambition and singular sense of musical style.