Rising above Sheffield station, the buildings of the Park Hill estate reach optimistically towards the sky – a hulking relic of the utopian housing schemes of the 1950s and 60s. The new musical by Sheffield musician Richard Hawley and Chris Bush is an ambivalent ode to those idealistic dreams, tracing a line from hopeful first tenants to dilapidation and gentrification.

Ben Stones’ austere design places three overlapping timelines in the same ghostly grey flat, its unadorned surfaces evoking the brutalist concrete outside. In the 1960s, Harry and Rose are among the first to excitedly walk the streets in the sky, embodying the hopes of postwar social housing. At the close of the 80s, Park Hill is a drab and decaying sanctuary for Joy, a young Liberian refugee. And in 2016, the newly refurbished estate provides a blank slate for southerner Poppy, fleeing heartbreak in London.

The past peeps through the cracks of the present … Rachel Wooding as Rose and Robert Lonsdale as Harry in Standing at the Sky’s Edge. Photograph: Johan Persson

The flat becomes a palimpsest of lives, the past peeping through the cracks of the present. In Lynne Page’s impressively choreographed group sequences, residents from across the decades bustle through the walkways around the flat and along the balcony perched above. There’s a sense of hidden histories, painting a chaotic portrait of the hundreds of individuals whose dramas have played out between these unforgiving walls.

Hawley’s songs – a mixture of familiar tunes from his back catalogue and new material written for the show – throb with wistful longing. It’s an apt soundtrack for the nostalgia, faded dreams and tentative new beginnings that characterise the estate, beautifully performed by the ensemble cast. Often, though, these melodies feel more like musical interludes than integral components of the drama. Likewise, the seams between the three narratives are awkwardly visible at times, straining the stitches that hold together the show’s ambitious collection of different elements.

But in the second half, as the dots connect between the three stories, the musical comes together. Bush gently questions Park Hill’s complex history and controversial present, celebrating Poppy’s new life while wondering at whose expense she can start over in a plush new flat. Mostly, though, Standing at the Sky’s Edge is a heartfelt exploration of home in all its guises.