It had only a brief run at the Pleasance this year, closing on Sunday August 16, but the 15th year of Nicholas Parsons’ Happy Hour in the courtyard’s Cabaret Bar was only curtailed because the 91-year-old star of the airwaves and the West End stage had other matters on his Edinburgh agenda. There were the usual recordings of the perennial BBC Radio 4 panel game he chairs, Just A Minute, with chaps like Paul Merton and Giles Brandreth, who also have their own shows on the Fringe, vying to speak for 60 seconds without repetition, hesitation or deviation. One of those was even transmitted immediately after the Today programme in a schedule-smashing move.

And Parsons was also at the book festival, launching his memoir of the programme, Welcome to Just A Minute, which covers its history in considerable depth, contains contributions from participants including Brandreth and Jenny Eclair, and which was praised in this newspaper’s book review pages as the anti-thesis of a programme cash-in publication.

Most of this activity Parsons organises himself, rather than relying on minders, agents or managers, but his business still seems to baffle him slightly, as if he hasn’t brought it all upon himself. He reels off recent television programmes he has been involved in with a note of surprise the explanations.

“I’ve done Life on a Plate, where they take you back to a house you lived in earlier days and talk about the food you had, and a Celebrity Antiques Roadshow. And in Holiday of a Lifetime I went back to Dorset.”

He feels very fortunate still to be offered the work, he says, which allows him to live a comfortable life, because there were days as a young performer when he couldn’t afford enough to eat.

Given half a chance, of course, Parsons will tell a Glasgow-based newspaper about his time as a trainee engineer on Clydeside, entertaining the troops at anti-aircraft sites and becoming involved with Rutherglen Rep and working with Molly Urquhart and Duncan MacRae and the Wilson Barrett company. One of my octogenarian mother’s friends in Burnside claims to have dated him in the war years, I tell him. He concedes that is more than possible.

But Parsons is not one to dwell for longer that seems seemly on the past, and puts the longevity of Just A Minute down to his own willingness to help develop the programme rather than see it remain in aspic. Its topics and the way he chairs the show are subject to constant change, even if the format remains broadly the same.

“When any job starts you don’t know that it will be successful, and you have to treat every show as if it is the first. I never go into a recording on auto-pilot, and because there is no script I still get nervous and I still find it exciting to do.”

There is a more relaxed Parsons to be seen at his Happy Hours, which packs people into to the tiny venue because of its enviable tea-time slot and the quality of the guests it attracts. Comedians who long since stopped flyering their own shows will still take time to publicise their appearances with Parsons.

“In the evenings I look for people who have good shows and invite them on, but we get lots of requests to come on the show, and PR companies pitch for inclusion. It is very flattering.”

And is this punishing schedule tiring for a man in his tenth decade on the planet? Apparently not.

“I have a system. I work in the morning and after lunch I have a nap between 3pm and 4.30. Then I get ready for the show, and after it I can go out for the evening.”

And when you bump into Nicholas Parsons later, checking out a Fringe show, you may be sure he is always as dapper as his publicity pictures. Or your money back.

*Welcome to Just A Minute is published by Canongate at £9.99