As a venue specialising in new and rarely performed musicals, Hope Mill has brought a dash of Broadway sparkle to a rather sooty enclave of Ancoats. In just over a year of operation, the theatre has resurrected Parade, Alfred Uhry’s portrait of antisemitism in the US deep south, and let it all hang out with the hippy manifesto Hair. Now it presents the UK premiere of a gay love story set in the Pacific theatre of war.

The plushly scored piece by brothers Joseph and David Zellnik is an unabashed throwback to the golden era of Broadway, in which the creators have attempted to imagine “the show that Rodgers and Hammerstein never wrote”. Indeed, it’s the show that no classic Broadway team could possibly have written, as it deals with the subject of gay men in the US army at a time when the penalty for homosexuality was three years in military prison.

Facebook Twitter Pinterest Plushly scored … Yank! Photograph: Anthony Robling

Drawing inspiration from the oral histories in Allan Bérubé’s book Coming Out Under Fire, the show was first produced off-Broadway in 2010, a year before the infamous “don’t ask don’t tell” policy towards gay servicemen and women was finally repealed. If the British premiere doesn’t benefit from quite the same topicality, it retains some of the show’s crusading spirit now that the Trump administration has begun to roll back transgender rights established by President Obama.

Even so, it’s far less a politically motivated show than a touching variation on the Broadway verities of boy-meets-boy, replete with full band, fleet-footed tap routines and a histrionic outcome. It begins in the present day with the discovery of a wartime journal detailing a love affair between 19-year-old Stu and the more worldly Mitch, who looks out for him in a barrack room quick to sniff out and persecute anyone deemed to be a pansy. The pair are separated when Stu’s literary abilities secure him a secondment to the forces’ weekly magazine, Yank, something of a haven for gay men, where Stu flourishes under the mentorship of a defiantly out photographer named Artie. But even after surviving the hell of the assault on Iwo Jima, Stu and Mitch’s idyll of a little house in the midwest is scuppered by the fact that it’s still 1945 and any dreams of domestic harmony remain far beyond reach.

What most strikes you about this smoothly accomplished production is that James Baker’s direction, James Cleeve’s musical supervision and especially Chris Cuming’s choreography hit standards far in advance of what seems reasonable to expect from the fringe. There’s exceptional work from Scott Hunter’s wet-behind-the-ears Stu, Barnaby Hughes’s conflicted Mitch and Chris Kiely’s slightly poisonous Artie. But the chief honours go to the lone female, Sarah-Louise Young, who portrays every mom, sweetheart and radio idol that helped to get these brave, frightened men through the war.

At Hope Mill, Manchester, until 8 April. Box office: 0161-275 9141.