Come Tuesday night, the Swallows and the Amazons will have reached their moorings at Edinburgh's Festival Theatre.

When the curtain comes up, the exuberantly rival crews will set sail for Wildcat Island, in search of swashbuckling adventure on land and lake – and if recent showings are anything to go by, the audience, whatever its age, will end up yearning to be aboard with the characters created by Arthur Ransome in 1929.

Director Tom Morris – who recently won a Tony Award on Broadway for his production of War Horse – is no stranger to Edinburgh. Before taking up his current post at Bristol Old Vic, he was the creative driving force behind many a successfully radical Fringe production. Even so, he did wonder if this new musical take on Ransome's old-fashioned children's story would travel well, despite the rave reviews that greeted its 2010 Christmas season in Bristol.

"My first thoughts, when I looked at the tour schedule was 'why on earth would a family in Scotland want to see a play about middle-class English children playing about with boats in 1929?'. Actually, why would today's audiences in London, Leeds or Liverpool be keen..." He laughs, because he's seen the answer time and again. "We discovered – not just with our Bristol audiences, but with a classroom of London children who'd never been on a boat – that it still connects because it's about children playing. And more than that, it's about children wanting to play pirates!" The relish in his voice gives the game away.

Morris was, by his own admission, a kid who loved to have hideaways – places where his imagination could create worlds beyond every-day realms. He still has that zest for play, but now translates it into wonderfully astute theatre-making. His intellect simply rejoices in looking sideways at conventions, before romping off to find alternative ways of finding the timeless truths in a text. Luckily he had a couple of like-minded talents as co-conspirators on Swallows And Amazons.

"Actually, it all came about backwards and entirely by accident," says Morris. "I'd listened to Neil Hannon's songs, and I'd thought, 'There's a story-telling instinct in those songs and a sense of character.' Maybe that meant he could work in a dramatic context... so I started talking to him. We did have various false starts, with Steppenwolf and things like that. Then suddenly he said, 'What about Swallows and Amazons?' And here we are."

"Here", when Hannon, the genius behind the band The Divine Comedy, takes up this story, is London's Vaudeville Theatre and the background noise while we talk is the happy hubbub of an audience waiting to go into a matinee of Swallows And Amazons. Hannon merrily affects mock affront. "Tom told you about Steppenwolf, did he? I've painstakingly avoided even mentioning that. And he's saying all this is my fault? It's true – and I hope that that's a good thing."

The critical acclaim and unstinting praise from a tweeting/blogging public – like the box-office returns – indicate that Hannon's idea was a very good thing indeed. But why fix on a book that is, in its slang and its attitudes, so distant from our own times? Would any 21st-century parent, asked to let young children go off for a week of unsupervised outdoors rough-and-tumble in the Lake District, say "better drowned than duffers" (as the Walkers' father does) before letting them loose in a little dinghy?

Hannon agrees that such behaviour would probably raise ructions – and care orders – nowadays. But when he started reading Ransome's book as a bed-time story for his daughter, what kept surfacing was the power of the children's own imagination at play. "When you took away all the nautical stuff – the sailing jargon that most of us don't know – I realised that one of the reasons it appealed to me was its way of bringing you back to that childhood thing of taking your own imagination seriously. Of believing totally in what you're creating. Swallows And Amazons just has that sort of mentality, where you can look at an everyday object – like a bit of wood, or a scrap of cloth – and transform it into a mast and a sail, or a cutlass and a cloak."

Was this, then, the stuff of songs? Another in a succession of dry chuckles is the preface to Hannon's genial reply. "I really didn't know what I was doing when I was writing the music for this. I'd never done anything like it before. So basically I set out to write songs that I thought would be fun for the characters to sing and for the audience to hear. And I think I came up with some songs that are funny and silly. But there is, I hope, a deeper level. There are profound themes in this story, subtle themes about childhood and relationships and challenges, and hopefully I've written songs that provided some sort of emotional context."

Writer Helen Edmundson, meanwhile, had to capture the essence of Ransome's book – all 375 pages, full of 1920s vocabulary and much luffing and jibbing, plus a character called Titty – and making it into a workable script for a modern family audience. Where others might have taken out all obscure references and period lingo, Edmundson opted for a long, slow process of engagement with Ransome as a person and a writer.

"I don't do 'filleting'," she says firmly. "Instead, I immerse myself in everything to do with the book. Its location: he sets it in the Lake District. The time: it's 1929, and the language the children use isn't necessarily familiar. We don't get excited about having buttered eggs for tea! "But some things don't change. And you can see that during a performance. Children often sit very quietly for the first few scenes, just listening. Watching this all-adult cast playing children, and how ordinary objects, like a feather duster and a pair of secateurs, become a parrot... and it just seems to click that this is all about using your imagination. And then they do get caught up in it, and find it thrilling and magical."

She has noticed, too, that everyone cheerfully buys into the illusion that Stewart Wright – a 6ft 2in bearded chap who's a prop forward – is truly and believably seven-year-old Roger, the youngest of the Walker/Swallows children.

"We made it an absolute golden rule of the rehearsal room that no 'gimping' was allowed," says Tom Morris, referring to what he describes as "that awful tradition of adults trying to imitate a child physically. It's just horrendous. Instead we asked actors to be themselves – but to ask themselves what a child of that age would want, what they would be trying to achieve. To play the imagination of a child, really, but to play as truthfully and as deadpan as they could. It has to be serious in intention so that children don't feel patronised."

The cast, of course, also had to sing. Hannon was on the look-out for anyone "singing a bit too stagily. You have to get them to reduce the vibrato, think of singing as if you were speaking, and what's been nice is that everyone in the show has really enjoyed the songs. I think I was aiming for a show-stopping moment – but if the show resolutely refuses to stop, then so be it. It's probably better for the plot."

That the pace refuses to stop owes much to the sleight of hand of the stage crew who pithily described the lo-tech challenges of swooshing from lake to shore, boat to camp-fire as "like sewing milk". As the 13-strong ensemble of actors/singers/musicians prepares to set sail in Edinburgh, Hannon sets the seal on the show when he says "it really has got something for everyone. I know... such a cliche. But how wonderful to say that and be able to mean it."

As for his daughter, who prompted the whole business, now aged 10, she's seen it twice now. Loves it. Does Hannon have a favourite song? "It's like my own back catalogue. I drift from one to another depending on what mood I'm in. But I really like the main Swallows song because of the recapitulation at the end. By then, the audience has gone on the journey with you, and it's time for the Swallows and Amazons to sail on in all these other imaginations."

Swallows And Amazons is at Edinburgh's Festival Theatre from Tuesday January 31 to Saturday February 4