American theatre and film maker Nancy Meckler has a strong reputation for making drama of a highly visual and physical kind.

As co-artistic director, with Polly Teale, of Oxford-based theatre company Shared Experience, she has long nurtured a performative style which is, in her words, "very close to dance".

The Shared Experience aesthetic has garnered so many critical plaudits over the last two decades that the world of English theatre was shocked when the group lost every penny of its core funding as part of the bonfire of arts grants which has burned across England since David Cameron and Nick Clegg came to office. It is, perhaps, testament to the gulf in perception which exists between the axe wielders at the Arts Council of England and performing arts makers themselves that Ashley Page, outgoing artistic director of Scottish Ballet, has invited Meckler to direct her first ever dance piece, a ballet adaptation of Tennessee Williams's famous play A Streetcar Named Desire.

Meckler is no stranger to shifting classic texts from one art form to another; she and Teale have adapted such famous novels as War And Peace and Anna Karenina for the stage. However, her latest project – which is being choreographed by Belgian-Colombian contemporary dance maker Annabelle Lopez Ochoa – is of a different order, and, when I meet her at Scottish Ballet's headquarters in the Tramway arts centre in Glasgow, Meckler's fascination with the work is palpable.

The genesis of her Williams's ballet lies, she explains, in a visit Page made to the Kennedy Center in Washington DC some 11 years ago. "Ashley saw a production of George Eliot's Mill On The Floss which I directed [for Shared Experience] with Polly Teale. He was interested in the way that we worked with movement." Page's long-standing admiration for Meckler's work culminated in, typically for him, an experimental notion. "He wanted," the director explains, "to put together a theatre director who is already using movement with a choreographer who has never done narrative ballet."

It was Meckler herself who suggested that Williams's 1947 play has great possibilities for ballet. To her delight, Lopez Ochoa agreed enthusiastically. There have been dance works based upon the drama in the past, but Scottish Ballet is offering an entirely new piece.

The atmospheric power of the play – which film-maker Elia Kazan famously made into a movie, starring Marlon Brando, in 1951 – is undeniable. Set in a small apartment in a working-class district of New Orleans, it unfolds the increasingly dangerous relations between proletarian alpha male Stanley Kowalski and his sister-in-law, archetypal fallen "southern belle" Blanche DuBois, whom Stanley's wife, Stella, his invited to stay.

Working on this narrative with a choreographer whose background is in abstract, contemporary dance is not difficult for Meckler. Much of the physical movement of her actors in Shared Experience has been shaped by choreographer Liz Ranken, who is best known for her work with London-based dance-theatre company DV8.

"People will often say that the movement my theatre company, Shared Experience, does is very close to dance," says Meckler. "We often do adaptations of novels which are about very repressed characters, like Anna Karenina, or some of the women in War And Peace, or Mill On The Floss. We will often explode, suddenly, into a sequence in which you will see inside the head of the person. So, the actors will actually be moving their character's fears, dreams or aspirations."

It is an aesthetic, she says, which makes the ballet a very natural progression for her as an artist. "Working in that [visual and physical] way in my theatre, I often thought, 'If we had dancers, just think how much further we could take it.'"

The director has always seen adaptation in the broadest terms. Novels are taken as inspiration, rather than sacred texts. She has never felt compelled to honour narrative detail. With ballet, she explains, that vision takes on a new dimension. "It was a luxury that we didn't have to have words. I could just say, 'Okay, if we really want to understand about Stanley, and what he's like, how popular he is, and what a macho force he is, how about going to the bowling alley?' So, we have a big scene in the bowling alley, where we get to meet Stanley."

The bowling alley, which is Stanley's favourite place of recreation, is only mentioned in the play. Meckler was amused to be reminded that Kazan also visualises it in the movie. "This made me laugh because I had been trying not to look at the film as I didn't want to be influenced by it, but I took a look at the film at one point, and they go to the bowling alley!"

Talking of the movie, I wonder if its memorable visual imagery, and Brando's iconic performance as Stanley, in particular, have impacted upon the ballet. They certainly seem to hover over every production of the play I have ever seen. "I do feel that [the influence of the film] when you try to do it as a play," Meckler agrees. "It's really hard to find anybody to play Stanley Kowalski who fits the bill. I did produce it as a play several years ago. I think it's really difficult.

"The interesting thing, once you're doing it in movement terms," she continues, "is that you're not telling the story in the same way and the dancer isn't up against Brando, because he doesn't have to speak Brando's words and he doesn't have to do Brando's moves ... Here [with the dance piece] we can keep some iconic moments; for us, it's very exciting to have a dancer actually shout 'Stella!', because that feels very shocking in a ballet. But it doesn't have to be anything more than inspired by Brando because he doesn't have to speak the text. When it's an actor speaking the text, you can almost hear Brando delivering the lines, and you can see his choices. But our dancer doesn't have to make the same choices because our moments are different moments."

That liberty in characterisation extends to Blanche, too, says the director. "Williams was originally going to call the play The Moth. We thought about that a lot; that image of a creature which is very vulnerable and is fluttering towards the light, but if it gets too close to the light it will be burnt. We were talking about the light being desire, and desire is what attracts Blanche and helps her to survive, but it's also what she knows will kill her, eventually. We start our ballet with a woman fluttering under a lightbulb."

Not only that, but Meckler has radically revised the play's narrative structure. "The power of the play lies in the fact that Blanche's back story is revealed very, very slowly," she suggests. "That slow revelation of the past is not so satisfying in ballet. So, we've taken quite a bold step, in that we start from the beginning, when Blanche is 15 and meets the young man who would later kill himself."

Meckler and Lopez Ochoa are bringing together their disciplines – visual, narrative theatre and abstract dance – in a fascinating way. "We're thinking of it, not as a play, but as a battleground," explains Meckler. "We think of it almost as if Blanche and Stanley are fighting over Stella, to see who's going to get her. Blanche comes into his territory, where he is king, and he is worried that she's going to steal Stella away from him. At a certain point Blanche does try to get Stella to leave, and that's why Stanley turns on her and destroys her. He tolerates her until that moment.

"So, we have this rough space and a chorus. When the men and women come together, they're society. When they're apart, they're distinct male and female energies. Within that, Stanley is essence of male energy; which is heavy, testosterone-driven and needs to dominate. Blanche is essence of female energy; which is vulnerable, fragile and poetic ... We're giving the audience a completely different experience than you get with the play. I think that's really exciting."

A Streetcar Named Desire is at the Theatre Royal, Glasgow, Wednesday to Saturday, then touring until May 19. Visit: www.scottishballet.co.uk.