One of Dame Edna Everage's shows was called, in a characteristically cunning pun, The Last Night of the Poms and it is a measure of the showbusiness status she achieved that the Australian housewife was able to fill the building that provoked the joke: the Royal Albert Hall in London.

Now, though, admirers of the housewife superstar from Moonee Ponds are forced to contemplate the last night of Edna as the letters always anagramatically scrambled in her forename – E-N-D – come into sight. Barry Humphries, the megastar's creator and manager, has suggested that the tour about to begin in Australia will mark the final stage appearances in her native land.

Connoisseurs of comedy genius will hope that plans for the farewell show to come to London and Broadway are fulfilled because with a performer of this magnitude – as with Dame Joan Sutherland and Maria Callas – the audience wants and needs a chance to say goodbye and thank you. Or as it was once memorably put by the Australian cultural attache to the Court of St James, Sir Les Patterson, another character in the Humphries group, "to put your hands together warmly across her opening and give her the clap she so richly deserves". (Few have doubled entendres as inventively as Humphries.)

Dame Edna at the Last Night of the Poms at the Royal Albert Hall, 2009. Photograph: Mark Allan/Getty Images

When Dame Edna first appeared in London in the 1960s, she was misunderstood by some as a drag act. But, in a way perhaps matched only by Dustin Hoffman's transvestite turn in Tootsie, this was character acting of remarkable precision and depth, in which the shift of gender was almost incidental to the vocal and physical detail, the latter helped by Humphries' possession of unusually shapely legs for a man.

But the knowledge that there was a cock in the frock, as the clearly Humphries-influenced Priscilla Queen of the Desert later put it, was never a large part of the gag. What began as a joke about Australian suburban delusion – Edna was initially a kind of Melbourne equivalent of Beverly in Abigail's Party – gradually became a much edgier reflection on celebrity. Along with the artist Andy Warhol (who can be seen as a character actor of a less openly declared kind), Humphries precociously understood that, over the next few decades, fame would shift from being something rare and earned to becoming randomly available.

Decades before Big Brother and the internet, Humphries saw the humour in the unlikely and accidental celebrity. The biggest problem for the character comic is becoming trapped in a single vocal and visual joke – one reason that Paul O'Grady, for example, retired his Liverpudlian Edna, Lily Savage – but a spoof on celebrity has the advantage that fame naturally transmutes. Humphries brilliantly piled upon Edna all of the victories and defeats that contemporary celebrity offers: physical makeover, TV talkshow, volumes of memoirs, stadium venues, tragedy (the loss of husband Norm to prostate cancer), rehab and comeback. With each return, Edna was different, her genuine and increasing fame constantly feeding the material. Typically, the farewell tour now opens up a whole new set of jokes about showbiz retirement rituals.

Barry Humphries as Edna Everage, 1979. Photograph: Chris Barham/Associated Newspa

Humphries also employed his bespectacled heroine – again, well ahead of the curve – not just to send up fame in general, but to undermine so-called real celebrities. Edna could be extraordinarily overbearing and belittling to interviewees – dismissing their books and movies, requiring them, like kids at a party, to wear a badge provided by her sidekick and former bridesmaid Madge – in a way that, when Clive Anderson tried it under his own name, resulted in walk-outs and a shortage of guests.

Perhaps the most fascinating aspect of the act, though, was how tough Humphries could be on himself. Many more recent comic character actors have clearly learned much from Humphries in terms of total immersion in verbal and physical detail: most notably, Steve Coogan's Alan Partridge, Caroline Aherne's Mrs Merton and Sacha Baron Cohen's Ali G, Borat and Brüno.

Coogan and Baron Cohen have also followed the Edna model in allowing their characters a separate existence on the publicity circuit, giving interviews and publicising books. In Humphries' case, the effort of separation is so great that radio and TV producers have received telephone calls from the dame herself about the logistics of upcoming appearances, and the crew on her TV shows were instructed always to address the host as "Edna" between takes, rather than "Barry". Although Humphries now has such easy access to the character that, during radio interviews, I have watched him summon her simply by pulling the brim of his trademark hat over his eyes.

No other comedian, however, has used his comic persona to denigrate himself in the way that Humphries routinely does: assassination by character. In both a South Bank Show edition and in her autobiographies, Edna mocks Humphries, always referred to as her "manager", as a bitter failure who is forced to endure a showbiz career rather than the renown as an artist and novelist that he craved.

This additional layer of satire and unease helps to make Dame Edna one of the most complex and inspirational creations in the history of comedy. Of course, one of the satirisable habits of celebrities is that they announce much-trumpeted farewell tours and are then back on the road again in a couple of years. So many will profoundly hope that Edna's retirement is just another knowing joke.