Two years ago, a young Edinburgh theatre producer by the name of Rupert Thomson wrote a provocative article entitled Save the Festival, Axe the Fringe.

Thomson, pictured below, argued that a combination of a rise in commercialisation and a decline in artistic quality on the Fringe was threatening Edinburgh's position as the world's pre-eminent festival city.

He gave as an example his experience with an Italian theatre company he had shown around Edinburgh with a view to putting their work on at the Fringe. "They were keen to come", he wrote, "but eventually decided that the festival – and the Fringe in particular – 'didn't feel right': not enough serious theatre, too much comedy, too much emphasis on money."

One year on from that article, Thomson was putting his money, or at least his considerable energy, where his mouth was. The Summerhall building (formerly the comically named Royal Dick Vet School), on the southside of the city, was being sold by Edinburgh University. Thomson spotted an opportunity, in the midst of the building's sale, to turn it into a temporary Fringe venue.

The resulting, hastily created Summerhall 2011 programme was a great success. Headlined by the well-received, through-the-night Brazilian-British co-production Hotel Medea, the work Thomson staged lived up to his stated intention to present high-quality, international work which had artistic, rather than commercial, imperatives at its heart.

Now, with the backing of the building's new proprietor, Robert McDowell, Thomson has turned Summerhall into a permanent arts centre with an impressively extensive Fringe programme. Inevitably, given both its ethos and the nature of the carefully curated work it is presenting, the Summerhall Fringe programme finds itself compared with Aurora Nova, the acclaimed visual theatre festival-within-the-festival which ran at St Stephen's church from 2001 until 2007.

"Aurora Nova was inspirational", Thomson tells me. "Not only in the work that it presented, but also in the way it went about its business. The support it gave to artists was very important, because the Fringe is a big market place.

"That, of course, is part of its value, but it also means that it will naturally have a commercial edge, which needs to be resisted quite consciously if it's not to take over. We are less motivated by commercial imperatives, even though, of course, we've got to think practically. We've got a bar and café, and we want lots of people coming in and having fun. But the main thing is to facilitate the best quality work we can."

One of the companies attracted to Summerhall by Thomson's ethics and advocacy is Teatr Piesn Kozła (Song of the Goat Theatre), a group from Wrocław in Poland. Well known to Aurora Nova audiences as creators of the extraordinary shows Chronicles – A Lamentation and Lacrimosa, the company had declared that they would not be returning to the Fringe following their last visit in 2007.

"I chose to come to come back to Edinburgh because I met Rupert from the Summerhall venue", says TPK's artistic director Grzegorz Bral. "He explained to me that there is a big desire among many people in Edinburgh to change the Festival Fringe into something which is significant once again, rather than just being thousands of stand-up comedians and insignificant art. I trusted him when he said 'please come, because the Festival needs people who are honestly searching for a profound theatre.'"

There can be no doubting the profundity or the artistic quality of the two shows which TPK are bringing to Summerhall next month. Macbeth (August 9-11) and Songs Of Lear (August 12-24) bring the group's very particular aesthetic (which is inspired by the Polish theatre master Jerzy Grotowski) to bear on two of Shakespeare's greatest tragedies.

I saw the older of the two pieces, Macbeth, at TPK's own theatre, a former nun's refectory in a 14th-century monastery in Wrocław, in 2009. At that point, it was a fascinatingly physical production, full of beautiful, typically Caravaggesque imagery, and drawing on the Bard's script in a selective way which gave it a different, and intriguing shape.

"I can only say that Macbeth is much more mature than when we toured it in England in 2010", comments Bral. "It is much more condensed, and much more emotionally powerful."

The newer work, Songs Of Lear, dispenses with Shakespeare's dialogue in favour of a deeply emotionally affecting, indeed spiritual, performance of polyphonic song. "The performance we have created is almost in the form of an oratorio", says Bral.

"It has numerous songs which take us through the story of King Lear. There is no linear narration, there is no text. Instead, the piece is constructed entirely of songs which operate like small, dramatic poems. Each song is a small performance."

The songs, of which there are 12, have been written by two composers, Jean-Claude Acquaviva from Corsica, and Maciej Rychly from Poland. Acquaviva's songs stand in the tradition of "liturgical polyphony", Bral explains. Rychly's have their roots in the Fifth, so-called "Heretic", Gospel of Saint Thomas (also known as "Doubting Thomas"), which was discovered in Egypt in 1945 and is written in the Egyptian Coptic language. Consequently, Rychly has composed his songs in Coptic.

"One music represents the court, the kingdom and the harmony of the play", the director comments. "The other, Coptic music brings the break in the harmony, the tragedy of the drama. It introduces the audience to the dark energies in the play when King Lear decides to divide his kingdom between two of his daughters."

That, one suspects, will be music to the ears of those who long for a more artistic Edinburgh Fringe. Bral, like Thomson, could prove to be part of a revolution which drives the moneylenders from the temple.

For further information about the Summerhall Fringe programme, visit www.summerhall.co.uk