Since that first production at The Almost Free Theatre, in which Henry Woolf - a stalwart of Harold Pinter plays - played The Lad Himself, as he prepared to commit suicide in a Sydney hotel room with only a scrapbook of newspaper cuttings, a telephone and a bottle of vodka for company. Like the legend of Hancock himself, however, Williams's play has lived on.
The late Richard Briers played Hancock in a radio version of Hancock's Last Half Hour in 1988. At that time, Pip Utton, who revived Williams's play for this year's Edinburgh Festival Fringe, was still working as a jeweller, and it would be several years before he picked up a copy of the play in a second-hand book shop and go on to launch his acting career with a portrayal of a man friends told him he resembled.
Twenty-one years on, Utton has performed in solo plays as real-life characters from Adolf Hitler to Charlie Chaplin, with Charles Dickens and Winston Churchill en route. It was Hancock, however, who started it all.
"I was amazed at the level of affection there was for him," reflects Utton. "It was amazing as well how big he was. He was a megastar in the UK, and was as big as The Beatles. Even today, people who are maybe too young to remember Hancock will still recognise some of his lines.
"The play is powerful, both because Hancock is so familiar, and because he breaks down and disintegrates in front of you," he says.
For Williams, a key figure in the British counter-culture of the 1960s as a poet, playwright, performer and polemicist, Hancock's Last Half Hour was an early look at the curse of fame, one of his work's perennial themes. It was also written out of very personal circumstances.
"There was an old rock and roller who was in a play of mine, Remember The Truth Dentist, in the Theatre Upstairs at the Royal Court," Williams remembers of a play directed by the late Ken Campbell, who Williams acted alongside as Prospero in Derek Jarman's film of Shakespeare's The Tempest. "He was called Roy Martin. He dragged me into Foyles in Charing Cross Road and said you have to buy anything and everything on Hancock and write a play about him.
"I do remember that Hancock was the one piece of common ground I shared with my father. Fractious and curmudgeonly, he'd had his pelvis crashed in the war, he used to roar with laughter at Hancock, and I could see it was therapeutic. Though my father was hard to warm to, Hancock provided moments when I could warm to him, so I had a personal reason for valuing him."
On the surface, at least, Hancock's Half Hour has less of a revolutionary intent than some of Williams's other works. In the late 1980s and early 1990s, his trilogy of ecologically inclined epic poems, Whale Nation, Sacred Elephant and Autogedden, all made waves, either in lavishly published editions, on film or in performance in Edinburgh.
More recently, Roy Hutchins performed Williams's radically inclined Zanzibar Cats at the Fringe in 2011, when Williams was awarded a Herald Archangel.
This was followed by a volume of science-based poems, Forbidden Fruit, a biography of Shelley and a new epic, Royal Babylon: The Criminal Record of the British Monarchy.
Then there is Williams's ongoing alliance with The Poetry Army, a touring collective that performs his work in a way that has become a kind of conscience of the nation.
"The Poetry Army shows how many revolutions have begun with a poem," Williams says of the initiative.
Now aged 72, Williams's output shows no sign of drying up. His latest play, Killing Kit, about playwright Christopher Marlowe, received a performed reading at London's Cockpit Theatre in February. Mike Figgis, a film-maker and former member of radical theatre troupe, The People Show, has expressed a desire to direct it.
In the meantime, Hancock lives on in a way that personifies the figure of the tragic clown.
"Why are comedians so vulnerable?" Williams muses. "Vivien Leigh said it was much easier to make people cry than to make them laugh.
"It's not a skill that you can learn. It's a gift, and a gift can be taken back.
"Look at the tragic people who are no longer funny, usually because they've taken the devil's shilling and done TV commercials," he says. "Somehow, as if by some diabolic magic, they then become unfunny. Comedy has to be subversive, and can't embrace commerce's creeping meatball. Hancock was reactionary in many ways, but he was also anarchic."
Hancock's Last Half Hour was at the Assembly Rooms. Run ended