It might be a scene from a fairy tale. The Queen has already placed the bird’s head upon her own. Now, with a chesty laugh, she attaches the wings.

She lifts them and they flap – fragile, diaphanous things that catch the spring light coming in through the windows. She chuckles again.

‘I made them long ago, for an amateur performance,’ she says. ‘A blue tit and a great tit.’ Her English is like this: exquisite and particular, the product of the University of Cambridge and the LSE (as well as the Sorbonne and Aarhus).

‘And yet they look new. It’s always good when things look as if they’ve only just happened.’

She lowers the wings with a nostalgic shake of the head and I picture her as a girl, fashioning the costumes for a palace masque.

Queen Margrethe, now a white-haired 75 and the head of Europe’s oldest monarchy, is sitting in one of the unlovely fitting rooms of the Royal Opera House, choosing fabrics.

At her side is Allan Watkins, the veteran costume designer, and a tailor who’ll help turn the Queen’s vivid, colour-drenched sketches into ballet costumes.

Fairy-tale versus reality

Cinderella, which opens in Copenhagen’s Tivoli Gardens in June, will be the seventh professional production the Queen has worked on.

Her designs have also featured in two films – both adaptations of Hans Christian Andersen stories. Alongside her stage work, the Queen is a celebrated visual artist, widely collected and exhibited.

She corresponded with JRR Tolkien and helped to translate and illustrate the Danish edition of The Lord of the Rings.  

There’s a cosy, conspiratorial air in the room. At one point, the discussion turns to epaulettes. ‘I want the dangly ones,’ she says, then lets out a snort of laughter.

‘Yes, the dangly ones.’ She reaches a thin, jewel-heavy hand across the table and picks up a Jammie Dodger, which she munches with vim, washing it down with a swig of coffee.

A very personable queen

I find myself gently falling for this amiable monarch, with her cigarette laugh – ‘I smoke wherever there’s an ashtray,’ she has said in the past.

Her intelligent eyes dart behind a librarian’s oval glasses, her white hair is pulled back from a high forehead, and she bares straight, yellow teeth in a habitual smile.

Now the great-great-granddaughter of Queen Victoria, who can trace her line back to the 10th-century Viking ruler Gorm the Old, pounces on a piece of fabric – ‘Ah, that’s a beautiful blue!’ She helps herself to another Jammie Dodger.

‘It is extremely enjoyable to be working like this,’ she says.  

I’ve been perching in a corner, observing the Queen in action, but seize upon a pause in the proceedings to grab a few minutes with her.

I ask whether the story of Cinderella has any relevance in 2016. Do little girls still dream of being princesses? Or would they rather their fairy godmother turned them into Taylor Swift? ‘Little girls seem more inclined to dream of being princesses nowadays than they ever were before, at least as far as I can see,’ she says with a smile.

‘All little girls seem to want to be in pink tinsel with bits of gold and sequins all over the place.’ She pauses for a moment, rotating one  of her diamond rings on a long finger.

Future of royalty

‘It’s not for me to say whether royalty still has an aura –  I look at it in a fairly matter-of-fact way. When  I was a child I didn’t enjoy princesses in fairy tales in the least because I wasn’t that way. I wasn’t pink and tinsely at all.’

Queen Margrethe II will celebrate her 76th birthday five days before our own Queen turns 90. They are firm friends, and the Danish monarch’s voice grows warm when she speaks about her third cousin. ‘That is an extraordinary  occasion, isn’t it?’ she says.

‘She’s wonderful. I really admire the way she has lived her life, the way she continues to live her life. She’s so dedicated and she has a marvellous sense of humour.

'I’m lucky enough to know her privately and I do enjoy that sense of humour.

'I also think that in the later years, that sense of humour has come across to the general public in Britain much more than it used to. And I’m so delighted for her sake.

'I know that her faith is very important to her, but I’m sure also it’s her sense of humour that keeps her looking so very good, that keeps her wonderful, in fact.’

We go on to speak of another impending anniversary. Queen Margrethe is devoted to Shakespeare, and will be the guest of honour  at the Globe’s staging of Hamlet at Kronborg Castle in Helsingør (or Elsinore), on April 21.

‘I’ve enjoyed Shakespeare’s plays for a very long time,’ she tells me. ‘I was taken by my parents to see Hamlet at Kronborg in the early 1950s, with Richard Burton as Hamlet.

'I don’t suppose I understood that much, but it made a great impression on me.

'Since then, I’ve seen so many Shakespeare plays. I usually come to London in December and I always manage to see at least one. He’s got such depth and I love the language – it’s beautiful – and there’s so much to it.’

Living with 'duality'

The Queen had been delayed by ‘frightful’ London traffic in the morning; she’s already late for lunch. Now, as she rises to leave, I ask  whether she doesn’t sometimes think of the artist she might have been – without the hand-pumping and ceremony, the painful daily exigencies of monarchy. She shakes her head vehemently.

‘I’ve lived with this duality for many years now,’ she says, ‘and I feel that the duty that I have gives an edge to the fact that I like expressing myself in art, but the duty part of my life is nourished by the fact that I’m able to work in my art, able to produce something myself.

'I don’t think I can really separate the two influences – the two go more or less hand-in-hand.’ 

 The Queen’s path to the throne was far from easy – it needed an act of parliament, in 1953, to allow for female succession, after which Margrethe lived with the ‘horrifying’ knowledge that only her beloved father’s death would bring her to coronation.

Now, though, she is wildly popular in Denmark, and mother of two boys, one of whom will take on the title when, as she puts it, she ‘falls off the throne’.

I give an awkward, atavistic half-curtsey as she pulls a brown cape around her shoulders and flashes her teeth at me, letting out a last deep-throated chuckle.

As I walk past her bodyguards, rugged and relaxed and thoroughly Scandinavian, I turn back to look at the Queen, who is tucking a skein of white hair behind an ear as she takes a last squint at the fabrics on the table.

In fairy tales, we’re never given the specifics of the happily ever after, but for Queen Margrethe, surrounded by like-minded artistic types and blissfully happy in her work, I imagine it looks something like this.

Cinderella is at the Pantomime Theatre, Tivoli Gardens, Copenhagen, June 25-September 8 (tivoligardens.com)