You may know Top Hat as the most famous of the movies made by Fred Astaire and Ginger Rogers in the 1930s - but for the last three years it has also been a stage musical which has notched up a trio of prestigious Olivier Awards and bedazzled audiences across the country.

The show offers the same scintillating blend of great songs, breathtaking dancing, knockout performances, and jaw-droppingly glamorous sets and costumes that made the original film such a smash back almost eight decades ago.

This was the film credited with saving RKO Studios from financial ruin. It is the film which features Astaire's iconic Top Hat, White Tie and Tails number plus one of the most romantic dance sequences in movie history. It was the first of the Astaire-Rogers films to not already exist as a Broadway show: the songs - which include Isn't This a Lovely Day (To Be Caught in the Rain) and Cheek to Cheek - were written by no less important a figure than Irving Berlin specifically for Astaire to sing, and were instant hits and long-term classics. It's a musical which fizzes along between song 'n' dance numbers with moments of screwball comedy performed by some of the best comic actors of the day. It inspired standing ovations at its first wave of cinema screenings back in 1935. How could anything dare to follow in its nifty footsteps?

Well, it's a sign of just how elegantly and thrillingly the stage version has been realised that it has been given the wholehearted blessing of Astaire's daughter, Ava Astaire McKenzie. Despite the fact she and her father's estate have no financial interest in the project, she has become an enthusiastic champion of the show and has even been willing to grant a rare interview ahead of its return to Scotland later this month for the first time since before its West End run.

McKenzie was first approached in 2009, when the show's producer Kenny Wax outlined his idea and explained that he was having trouble convincing the Irving Berlin Music Company to grant permission to use the songs.

She says: "He talked to me about my feelings because it is so associated with my father that he was interested in my reaction. Since it had never been a stage show, I thought it was a wonderful idea so I wrote to the Irving Berlin Music Company saying I felt the timing seemed right, and I'd no objection. Never did I expect it to be as wonderful as it is, because they added many more Berlin songs to it which was great because there were only five in the movie."

Only one aspect of the idea troubled McKenzie. "There was always one hesitation on my part, which I made clear to everybody -that I would not have been happy seeing the leading man trying to play my father rather than the character Jerry Travers. And they've all made it their own. So I'm pleased."

That said, the songs were written specifically for Astaire to sing. Berlin upped sticks from New York to serve as composer in residence, and brought with him what he called his "Buick" - an oversized upright piano with a mechanism for shifting the keyboard and transposing his melodies into any key - since Berlin had taught himself to play piano in only one key. Also, there was a collaboration between Astaire and Berlin: Astaire was keen to recycle a tap routine from a disastrous stage show and his description of it inspired the composer to produce the glorious Top Hat, White Tie and Tails.

Was Astaire at all proprietorial about the songs which were written for him to sing - not just in Top Hat, but also in subsequent films when he introduced Gershwin and Jerome Kern standards?

"I don't think he felt proprietorial about anything," says McKenzie, pointing out that her father was always delighted when others - such as Tony Bennett - sang some of the 40-odd songs he had composed.

Alan Burkitt and Charlotte Gooch, who play Jerry Travers and Dale Tremont, may not be playing their characters as Astaire and Rogers did, but other aspects of the movie have been retained in the stage show - not least the feathered frock which Rogers designed for herself to wear in the swoonsome Cheek to Cheek number. The filming of this particular dance was the source, says McKenzie, of the rumours of a rift between the dance partners - because Astaire reduced Rogers to tears with his angry outburst when wispy feathers kept detaching themselves from her gown and floating off in his direction.

While he was singing "Heaven, I'm in heaven .." Astaire was actually, as he later described it, in hell. "It was like a chicken attacked by a coyote," he said. McKenzie says: "Most of the time they got on well but he did lose his temper on that occasion because he had not seen the dress - only sketches of it - and nobody took into account that those feathers were not going to stay put. They literally blinded him, got up his nose, and in his eyes - and he lost his temper, which he would, if anything got in the way of his work. He had a quick temper about that. So I think that whole rift thing is based on that.

"Of course you know the end of the story is that after it was all over, daddy and Hermes Pan - the choreographer and his best friend - presented Ginger with a little gold feather from Cartier for her charm bracelet and sang a song to the tune of Cheek to Cheek that went 'Feathers, we've got feathers ..' and he did in fact write a note saying something like 'Dear Feathers'."

Understandably, McKenzie has been paying close attention to the Cheek to Cheek dress in the stage show. "There have been two different dresses - one has more feathers than the other, but I did watch to see if they were coming loose, and last time just a few were floating around!"

Top Hat is at His Majesty's Theatre, Aberdeen, from September 23-October 4; the Festival Theatre, Edinburgh, from October 7-18, and the King's Theatre, Glasgow, from December 2-13.