Many of their most celebrated collaborators - Tony Hancock and Harry H Corbett and Wilfred Brambell from Steptoe and Son - have long since departed, but Galton and Simpson are still going strong. They are working together on a new Paul Merton series for Carlton, and Galton (in partnership with John Antrobus) is scripting a new sitcom about a sanatorium for broadcast on BBC1 next year.
Good writers never die, they just write about sanatoriums. Galton rolls back the years as he enthuses about the new project: "Obviously, you don't have people coughing up their lungs and dying, but anything can be made funny." Who, after all, would have thought there was much comic mileage in a series about two lonely, bickering rag-and-bone men?
A sanatorium is, ironically, where it all started for Galton and Simpson. They first met as teenagers in 1948 at Milford Sanatorium where they were both receiving treatment for TB. They decided to write some material for a hospital radio service being used as occupational therapy - and one of comedy's most enduring partnerships was born. Chucking in their jobs - Galton had been employed at the Transport and General Workers' Union, and Simpson had been working as a shipping clerk - they graduated through church concert parties to the BBC, where they were working professionally by 1951. The very next year, they met Tony Hancock, for whom they proceeded to write 101 radio episodes of Hancock's Half Hour and 63 episodes of the television version.
Tapes of these shows and of Steptoe and Son still do a roaring trade. Why do they still appeal to generations born long after they stopped being made? "Without getting portentous," Simpson observes, "the characters we write are not of any particular era. Their attitudes have been around for 2,000 years. It's about people aspiring to better themselves - and that's not just particular to the 1960s. The Hancock character is there in Dickens. People can still identify with these characters, they're recognisable. The same applies to Steptoe. Inner-city conflict within families is not peculiar to any era or country".
Although now both genial, grey-bearded men in their mid 60s - Galton was born in 1930, Simpson in 1929 - they still keep their fingers on the sitcom pulse. "There are some great comic creations around," Simpson reckons, "look at Father Ted or Absolutely Fabulous or Drop the Dead Donkey. For years, it was all domestic comedy - which we both hate. It became more adventurous and iconoclastic with The Young Ones and Rab C Nesbitt."
Galton, like a well-drilled double-act partner should, takes up the story. "If there's any secret, it lies in the characters. In those domestic sitcoms, there are no characters, they're all just stereotypes. Ab Fab and Father Ted have wonderful characters - and that's half the battle."
"Laughs come from the actions between the characters," Simpson adds. "You don't need a joke to get a laugh; things become funny because you know the characters. When we started, people couldn't understand that you could write a half-hour comedy without gags."
Galton and Simpson, of course, helped to change all that, Their material has been hugely influential. Critics have gone so far as to compare the best of their writing with that of Harold Pinter. "Hancock went to see The Caretaker when it first came out," Galton recalls, "and he came back and said to us, `Christ, you've been writing this sort of stuff for years.' "
And they continue to do so to this day.
The BBC Radio Collection's double cassette of "Hancock's Half Hour 8" (pounds 7.99) is released on 4 Nov. Hancock is currently being repeated on BBC2
3 HOSPITAL DRAMAS
Flowers of the Forest (Sat BBC2) Harrowing "Screen Two" about allegations of satanic abuse in the Highlands.
Billy Connolly's World Tour of Australia (Mon BBC1) Down Under gets the Big Yin tourism treatment.
Cracker (Mon ITV) Robbie Coltrane's psychologist on a murder in Hong Kong.
Blind Date (Sat C4) It pains me to say it, but isn't Cilla's camp classic showing its age now?
Police, Camera, Action! (Mon ITV) Enough flashing blue lights, already!
Two Fat Ladies (Wed BBC2) More "personality" chefs; Keith Floyd has a lot to answer for.
Casualty (Sat BBC1) The venerable elder statesman of the genre, still in fine fettle after all these years.
ER (Sat C4) The flash, sexy American swaggerer. Blood pressure high.
Staying Alive (Fri ITV) The cocky new kid on the block. The lives and loves of six student nurses.