It is just before midnight and Dame Helen Mirren is wiping deathly pale make-up off her face and brewing a cup of tea in a bare dressing room in the middle of a Greek wood. A path leads up through the pine trees to the extraordinary 2,400-year-old amphitheatre of Epidaurus, where the National Theatre’s production of Racine’s tragedy Phèdre is the hottest ticket of the summer festival season.

Mirren is arguably the biggest international star to perform at the 11,000-seat theatre since the opera singer Maria Callas in the 1960s, and she is once again playing a queen, albeit a rather more expressive one than her Queen Elizabeth II, for which she won an Oscar in 2007. But there is nothing regal or diva-like about her.

“You want to know if Dame Helen double dips her pitta bread into the tzatziki next to the stage hands?” asks one member of the company. “Absolutely, she does.”

Backstage after the dress rehearsal, Mirren has only one request. A few minutes earlier as she was collapsing, fatally poisoned, at the end of one of the most psychologically and emotionally draining roles in theatre, she had a thought: “A glass of champagne, that’s what I’m going to have when I get back to the hotel. I think I’ve deserved it.”

The champagne is welcome but for Mirren and the rest of the 30-strong touring party (including 12 actors, a crack squad of technicians, a voice coach, wigs, lighting and make-up people) the real reward is the chance to perform and work in one of the world’s most evocative venues.

“You are always nervous that you are about to make an enormous fool out of yourself, but I was so excited by the idea of treading on a stage that people were acting on all those years ago,” Mirren says. “It is magical.”

The steeply raked stone theatre is set amid hills, two-and-a-half hours’ drive south of Athens. Behind the round earth stage the ground falls away to olive groves, and beyond them, rugged mountains that turn purple at dusk, when performances traditionally begin.

Stag beetles, spiders, bats and cicadas wheel and crawl over a crowd who behave more like football fans than a reverent West End audience. It is a special place, says Nicholas Hytner, the director of the National.

“With the best will in the world, it’s not the same as going to Salford or Newcastle, much as we love going there too.”

Quite so. The company has enjoyed all-night outdoor drinking sessions, dawn swims, an island-hopping boat trip and a much talked about arm-wrestling bout. The actor Dominic Cooper, who is something of an expert at frolicking about in Greece after Mamma Mia! and is a self-proclaimed arm-wrestling champion, challenged the enormous Stanley Townsend, who plays his father Theseus. Townsend crushed him.

Hytner regards the whole trip, which ended with two sold-out performances at the weekend, as “essentially a fantastic, inspiring treat” but one with a serious additional purpose.

“I think that we do not have enough contact with the Continent and I want us to be more in touch. A lot of my continental colleagues say that British theatre is separate and mysterious and we don’t join in.”

The National has visited Epidaurus six times over 27 years, mostly with Greek dramas. Phèdre, which recounts the destructive obsession of Theseus’ queen with her stepson, is set in that world too, but filtered through the eyes of a 17th century French playwright and the freewheeling translation of a British poet, Ted Hughes.

Half the London critics loved the production, others were less convinced and some were outright hostile.

Mirren does not know, because she only reads reviews “when horrible people send the bad ones to you”.

Last month the production broke new ground when a live broadcast of it was beamed into 270 cinemas around the world, this time to unanimously good reviews, which were rather sidelined by news of Michael Jackson’s death breaking the same evening.

The principal challenge for the actors in Epidaurus is to recalibrate their performances from something that works in cinema close-up and the relative intimacy of the Lyttelton Theatre on the South Bank to something that can be heard 60 rows up. Despite the theatre’s fabled acoustic, it is “extreme sport acting” Hytner says.

Maria Panagiotopoulou of the Athens and Epidaurus Festival has seen “many great actors and actresses trembling with fear before they go on because this theatre kills actors. But these ones were excellent. British actors are the best in the world.”

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