Inside the new Edinburgh International Festival showroom at Ingliston

We are in one of three performance spaces carved out of the Lowland Hall at the Royal Highland Centre in Ingliston, this one a conventional “black box” shape with its own temporary raked seating, walls and roof, but built with a stage as wide as the Edinburgh Festival Theatre, about 30 metres.

It will host Theater Basel’s satirical Swiss-German variation on My Fair Lady, staged in a tatty English language learning laboratory run by an eccentric Hungarian linguist, where the set runs from a bank of 1970s-style typing booths on the left to a white baby grand piano by the stairs on the right.

In a space most people would know as an agricultural hall at the Royal Highland Show, Mills and his team have constructed a little theatre empire of their own, in what is probably his most ambitious Festival venture yet, a kind of über-Fringe of cavernous proportions, seating between 400 and 800 people.

It’s taken something like three miles of “really substantial cabling”, says the Festival’s technical director, John Robb. Gleaming metal trusses more than 50m long run the length and breath of the building; vast black drapes hang down from end to end of the hall. There are undoubtedly several miles of scaffolding poles. In the venue’s bar, a flight of six giant white doves, the Festival’s emblem, hover on transparent panels overhead. Out of sight, there’s a set of mirrored green rooms for performers. Giant billboards for the shows run along the side of the building.

The preparations have included 24 acoustic readings of the hall to test for any interference noise from aircraft at nearby Edinburgh Airport. “It doesn’t seem to affect the space at all,” Robb says, and sure enough, there’s not been a whisper of aircraft noise noticeable during two visits, albeit there has been some deafening hammering of metal on metal on the first trip here.

“These are theatre experiences,” says Mills, “the likes of which you simply can’t get other than in a space like this.”

The set for 2008: Macbeth is a two-storey house with four open rooms facing the audience at one end of the hall. In the centre is the French production of Les Naufrages du Fol Espoir Aurores – The Castaways of the Fol Espoir (Sunrises), adapted from a Jules Verne adventure, with its own elegantly arched, recreated early 20th-century dance hall, stretching away from the audience, again with its own roof. To simulate daylight streaming down through glass, there is a hidden bank of 300 to 400 lighting tubes.

With a running time of four hours including an interval for Meine Faire Dame, one of the Festival’s boasts is that the space contains “the most comfortable temporary seating in the country”, with extra leg room and back support, and certainly a surprisingly soft feel when you settle back in your seat. “It’s not a torture to sit in them,” says Mills.

2008: Macbeth, which opens on Saturday, and Meine Faire Dame will run in tandem for several days during the Festival, with alternating matinee and evening performances, but not at the same time – insulating them acoustically from each other would have been far too costly. Les Naufrage du Sol runs in the second half of the Festival, with the space only dark for a couple of nights.

Artists over the last 20 or 30 years, whose work is represented here, have pushed out the boundaries of theatrical performances, said Mills. “The three spaces are at some level quite conventional, but none of them would fit into our conventional theatre spaces in Edinburgh.”

For those looking for new creations out of Edinburgh, none of these productions is a world premier. “I would not have done something like this with newly commissioned work,” says Mills. “When you have got all the added technical issues the last thing you need is an additional sense of adventure.” It meant that Robb could take precise measurements of existing sets and put them together like a jigsaw.

But what it will do, says Mills, is showcase the work of three directors from three different generations, all “leaders and innovators” in European theatre. The 1939-born French director Ariane Mnouchkine founded Théâtre du Soleil, the avant-garde Parisian stage ensemble bringing Les Naufrages, in 1964, fuelled by the student uprisings of the 1960s; her work has not been seen in the UK for about 20 years. The Swiss musician and opera director Christoph Marthaler, with Meine Faire Dame, was born in 1951, while Poland’s Grzegorz Jarzyna became director of the TR Warszawa company in 1998, at the age of 30.

2008: Macbeth was first staged in a former arms factory warehouse outside Warsaw, and then under the Brooklyn Bridge in New York, using the same set. It is described as a visceral, violently physical production deplying multi-media devices, with actors armed with Uzis, and banks of television screens. It carries an anti-war message in the context of America’s military campaigns in Iraq and Afghanistan, the invasion of one culture by another; battles take place in front of a mosque.

The two other shows are more satirical, in different styles. Meine Faire Dame – ein Sprachlabor, already “basically sold out”, says Mills, is a contemporary reinvention of Pygmalion. Fife-born actor Graham Valentine – far better known in Germany or France as a star of musical theatre than in Britain – will make his stage debut in the Festival apparently playing both Eliza Doolittle and Professor Higgins in a Dadaesque production with a soundtrack running from Bryan Adams to Wagner. The satire is in the setting of the language class where everyone wants to speak “the Queen’s English, or speak perfect English,” says Mills, but “would you want to learn English from someone as unhinged and weird as Henry Higgins?”

Over 16 days, a team of about 70 people built the three sets side by side, filling the 4,500 square metres of the hall with 50 tonnes of equipment. At the front, the Macbeth set is a terraced house, from back stage a glittering pin cushion of scaffolding. When its run ends, it will be removed, and its bank of seats rolled forward to face the set for Les Naufrages.

Théâtre du Soleil’s show connects to Macbeth loosely in that it is also “cinematic”, but in a far gentler style, dating from the early days of silent film, using the technology of 1910s rather than the 2010s. In a company where “everyone does everything, backstage, front of stage,” audiences join in the “sense of revelation, the process of theatre-making, the anticipation of theatre magic,” said Mills, as the story evolves from the making of an amateur film to a castaways’ trip around Cape Horn.

The Lowland Hall adventure is backed as part of the London 2012 Festival. Buses for the site leave the east  end of Queen Street for a 45-minute journey, with time for a drink before the show; people have been encouraged to buy matinee and evening performances on the same day.

In this “time and motion study” of interlocking shows and sets, the Festival has learned an enormous amount about the use of the space, Mills says. It was first tested for the demotic, immersive Romanian production of Faust, which the Festival hosted at the Lowland Hall in 2009; Mills has little doubt the Festival will be back here in future years.

“That was an amazing experience for our technical team, and this is several steps further than that. The more we learn about this space, and the more we work closely with the management of it, the more they will want us here and the more we will want to be here,” he says. “What it means is myself and future Festival directors will be less constrained by the theatres in Edinburgh itself. We sold Faust out, we could have sold more performances of that.

“We’re in a sense inventing an arts centre in the centre of the Festival, it’s a heartbeat in a body that’s very vibrant. In a year where the eyes of the world were on the UK, it was very important to do an international festival of genuine scope and scale, and that’s what we’ve done.”