Play sees Doctor Who and Star Trek actors join forces

“It’s about three characters with no past and no future who find themselves just arriving,” says McCoy.

“They don’t know where they are, if they’re in a joke or what the joke is, so they explore and try to discover. It’s an excuse to tell hoary old jokes and discuss them, really.”

In fact, the play itself is structured along the lines of the joke mentioned above, with McCoy playing the Irishman, Richard Oliver as the Englishman and Picardo as the Scotsman. Oliver – an actor who also runs the Theatre Space in Winsford, Cheshire, where A Joke previewed – was recruited by the play’s writer and director Dan Freeman.

Freeman is most well-known as the creator of the acclaimed sci-fi audio series The Minister Of Chance, and McCoy agreed to come in on A Joke because of the trust established while working with Freeman on the series; fellow sci-fi alumni including Paul McGann, Philip Glenister and Jenny Agutter have also been involved.

“I’ve enjoyed working with Dan over the years, so when he asked me I said yes,” says McCoy. “I’ve always found his writing to be witty and of some depth. A Joke is about humour and life, really, and whether there’s anything else out there. Is there anything else, or are we all just part of this joke? It’s the kind of debate we all have.”

It was Freeman’s idea to cast Picardo, although McCoy did the asking, the pair being old friends from the sci-fi convention circuit in America. “It was an irresistible offer to appear at the Edinburgh Fringe,” says Picardo, “and also to go to Scotland and play a character called the Scotsman. That sounds like it’s asking for trouble, but fortunately my character is an American who claims to be of Scottish heritage – although it’s perhaps a spurious claim. I have the licence to do a Scottish accent, but a terrible one, which gave me the confidence to do it. The play is a vaudeville that turns into something more serious at the end.”

An Edinburgh debutant at the age of 63, Picardo has visited the Festival before as an audience member and is excited about the challenge ahead.

The relationship between television and theatre works differently in the US – each industry is largely based on opposite coasts, so opportunities to move between them are fewer than in the UK– however he’s no stranger to the stage. In the late 1970s, when he was still in his late teens, he took two major roles on Broadway, first in Albert Innaurato’s long-running sexual identity comedy Gemini, and then as Jack Lemmon’s son in Bernard Slade’s Tribute.

“For two consecutive Broadway seasons I had probably the best juvenile roles there were for an actor,” he remembers. “Then I moved to California to recreate my role in the film version of Tribute, I started working in film and television after that, and 38 years blew by! I’ve continued to do theatre in California, but the attitude towards it there is as a second-class citizen.

“People admire a screen actor if they have theatre skills, but it’s looked down upon by the industry as being not a ‘real job’, in the way it isn’t in New York or the UK.”

The 73-year-old McCoy, on the other hand, is a veteran of both the stage and the Edinburgh Festival; in fact, outside of the Doctor and his role as Radagast the Brown in Peter Jackson’s Hobbit trilogy between 2012 and 2014 (Jackson is a fan of Who and McCoy), his prolific and wide-ranging stage career is the outstanding element of his CV. “The very first time I played the Fringe was in 1972, in the venue they’d built in Waverley Station for The Great Northern Welly Boot Show,” he says. “We were in the smaller venue downstairs, and Billy Connolly came to see our show, which is when we became friends. I’ve also done two International Festival plays, we took Calderon’s [Pedro Calederon de la Barca’s] Life is a Dream to London and New York after Edinburgh, and in 1996 we did John McGrath’s A Satire Of The Four Estaites.”

McCoy’s also staged a number of one-man shows on the Fringe, for example 2002’s Hello Dali, in which he appeared in character as the great surrealist. “For me, Edinburgh is the best place to be in August,” he says. “It’s a wondrous experience, and everyone talks to everybody. My granny lived in London during the war, and she used to tell us that the bombing was terrible, but that the one good thing was that everyone talked to each other, regardless of class. In a way, it’s like that in Edinburgh.” Elsewhere, McCoy played the fool opposite Ian McKellen in the Royal Shakespeare Company’s King Lear in 2007, and more recently he appeared in Plume at Glasgow’s Tron Theatre in 2012.

It’s almost a contractual obligation to ask McCoy a Who-related question, and the recently announced one about the latest incarnation of the character being a woman is the most obvious.

“When the casting of Jodie Whittaker was announced, I realised this could be really exciting and interesting,” he says.

“I sent her a message saying ‘one small step for woman and one giant leap for womankind’, to welcome her to the world of space. Let’s see what happens.”

• A Joke is at theSpace on Niddry Street until 26 August. Today 1:55pm.