Something fishy is going on in theatreland. There’s a meeting of the Critics’ Circle but one of the members hasn’t shown up. Every time a concerned journo goes to investigate, they disappear too. At the mystery’s heart is Edward Lionheart, an actor in the grand tradition. He’s been assumed dead for two years, but now, in revenge for a lifetime of bad reviews, it seems he’s bumping off the critics one by one.

The clue to it all could lie with his daughter, Edwina, whom we find leaving lilies at his memorial statue. ‘Well, the brilliant Peregrine Devlin,’ she says to one of the critics. ‘Wielder of the brutal aphorism, master of the killing phrase: my father’s murderer!’ Before long, the finger of suspicion will point in her direction. These are the opening scenes of Theatre of Blood, the classic 1973 horror-comedy newly re-released on Blu-ray, and starring a post-Avengers Diana Rigg. Now 20 years a dame, Rigg is making her Edinburgh Fringe debut with a compendium of critical put-downs based on her 1982 book, No Turn Unstoned (subtitled ‘The Worst Ever Theatrical Reviews’).

This evidence would suggest her hatred of critics is deep and longstanding, but the reverse is the case. Oddly, it’s only when I mention Theatre of Blood that the thought even occurs to her. ‘I’d not made that connection,’ she says. ‘It’s purely coincidental. I don’t have it in for critics and I never have. The genesis of the book was nothing to do with tilting a lance at critics. It was putting them into the context of theatrical history.’

She does admit that you couldn’t read No Turn Unstoned without a sense of humour. It quotes Benedict Nightingale describing Simon Callow playing Mozart in Amadeus ‘as a goonish cross between a chimp and a donkey’. Julie Christie’s local paper said she ‘should never, ever, be allowed to sing unaccompanied on stage again’. Even John Gielgud does not come out unscathed: Ivor Brown said he had ‘the most meaningless legs imaginable’.

But Rigg acknowledges that in her line of work, criticism goes with the territory. ‘Critics have to sit through an awful lot of rubbish and you feel really sorry for them,’ she says. ‘In fact, I’ve been in a play where I felt sorry for the critics.’ Not only that, but she reckons, historically, critics have done an invaluable job. ‘We depend on the critics to give us a glimpse of what happened. Bernard Shaw championed Ibsen, who got the most terrible notices for his plays. Kenneth Tynan championed young writers and as a result the theatre has changed radically. The number of young writers we have now is wonderful and that is as a direct result of Tynan lighting the blue paper under all those vapid drawing-room comedies. It’s not about knocking critics and never has been.’

Not that it doesn’t sting when a bad review strikes. The Edinburgh Fringe must generate more criticism per actor than anywhere in the world. There will be many a Fringe performer in the coming weeks who shares the pain Rigg felt when US critic John Simon said she was ‘built like a brick mausoleum with insufficient flying buttresses’. For all her championing of critics, she can give as good as she gets and still seethes at the memory of a Guardian review by Nicholas de Jongh (she calls him ‘Nicholas de Wrong’) that rubbished her performance as Cleopatra in a 1991 production of All for Love to devastating effect.

‘He had no right to do that,’ she says. ‘He had a witty turn of phrase, always at somebody else’s expense, and he got himself a following. He was dreaded, but he seemed to take a delight in destruction, which made good reading but was no good for the theatre.’ When a somewhat contrite de Jongh turned playwright in 2008, he told The Guardian he expected rough treatment by the actors he had once savaged: ‘I said Diana Rigg had a shot at the part and killed it stone dead. I understand why she’d loathe that.’

Now at the age of 76, this keen theatregoer can’t wait to wind up in the midst of Edinburgh’s cultural melee and to check out other acts. Despite her level of experience, she has never stopped learning. ‘I went to see Heartbreak House at the Almeida starring Penelope Wilton. I’d done Heartbreak House and was not at all satisfied with myself and Penelope Wilton got it right. I was too pushy in the part and she was wonderfully cool. You do learn. Anybody who acts on the back foot irritates the living daylights out of me when I see them on stage.’

Although she has never done the Fringe, she knows Edinburgh from the time her daughter and fellow Doctor Who star Rachael Stirling was at university in the city. No Turn Unstoned was a piece she first performed on the American college circuit (‘Mrs Thatcher was going around at the same time and earning probably 50 times more than I was’), but only recently has she returned to it, this time as a way of raising money for unsubsidised theatres. Adding recent reviews to the historical material, she’ll be reaching a new generation on the Fringe.

Among them are sure to be fans of Game of Thrones, in which she plays elder stateswoman Lady Olenna Tyrell. Once the Fringe is behind her, she’ll be heading to Dubrovnik for more filming, as well as passing on some crucial down-time skills to her younger co-stars. A long-time games player, she’s been introducing them to everything from complex mind games to tavli, the Greek equivalent of backgammon. ‘There’s a lot of sitting round and I’m a games person,’ she says. ‘I used to have a bridge session in my dressing room at the Old Vic on matinee days. I’m really grateful for Game of Thrones. It’s something wonderful to happen to an actress of my age and Dubrovnik is astonishingly beautiful.’

First though, in true Fringe spirit, she’d like No Turn Unstoned to fly the flag for the artform so central to Edinburgh in August. ‘I hope it generates courage and pride in the profession of acting. I’m going to have a good time.’

Diana Rigg: No Turn Unstoned, Assembly Checkpoint, Bristo Place, 0131 623 3030, 14–23 Aug, 1.20pm, £12.50–£15 (£10–£13).