Brian Viner: It's time to play the music (not a moment too soon). The Muppets are back!

At the National Television Awards on Wednesday, a small green puppet in a tuxedo, standing behind a glittering podium, announced the award for Best Entertainment Presenter, lamenting in his preamble the fact that there were no amphibians on the shortlist. The over-35s in the audience at the O2 chuckled, but a good chunk of the under-35s looked puzzled. It wasn't that they weren't comfortable with a vertically challenged, bow-tied presenter shouting at them, but this wasn't Dermot O'Leary. This was Kermit the Frog, only vaguely familiar to them, and yet restored, some would say, to his rightful place at the heart of mainstream popular culture.

The Muppets are back. The new Muppets film, already doing terrific business at the American box office, opens here next month. When the project was announced there were plenty, within as well as outside the movie industry, who felt that Kermit and his friends had had their day, that in the age of 3D technology and the extraordinary wizardry of Pixar, Miss Piggy batting her eyelashes would be a clunking anachronism. On the other side of the equation, some veteran Muppets performers, such as Hereford-born Frank Oz, still the voice of Miss Piggy and Fozzie Bear, were worried that in striving to make the Muppets relevant to a modern cinema audience, the integrity of the characters might be compromised. Early scripts did nothing to dilute their concerns. A fart joke was rejected as "too cheap".

The finished product, however, is by all accounts a triumph. Variety welcomed the film's blend of "wised-up, self-reflective humour with old-fashioned let's-put-on-a-show pizzazz", and The Hollywood Reporter's critic predicted that it would accomplish its goal of pleasing old fans and winning new ones. The latter objective is plainly the more important of the two. While "old" fans of the Muppets might think of themselves as being as ageless as their favourite frog, the reality is that it is their children and grandchildren that Kermit must charm and Miss Piggy seduce.

Still, the original fans have the immeasurable consolation of knowing that they were in at the start, in 1976, when The Muppet Show brought unprecedented wit and fun to Sunday teatimes in a decade scarred by industrial unrest and badly in need of light relief. The manoeuvrings of Bernie the Bolt on The Golden Shot had once represented the pinnacle of Sunday entertainment on British television; now it was the joyous Muppets orchestra, the outrageous diva that was Miss Piggy, the wise-cracking curmudgeons Statler and Waldorf, and the ridiculous stunts of the Great Gonzo (inspired, so it was said, by Evel Knievel, another name to conjure wistful nostalgia among those of us who knew kipper ties and three-day weeks).

The simple premise of each programme was that the Muppets would organise and perform a variety show in front of a live audience, with Kermit as master of ceremonies, and a human guest star such as Elton John. That was it, and yet remarkably, at a time when every hard-hitting episode of The Sweeney was dissected in the school corridor the following day, there was no loss of face in owning up to loving The Muppet Show.

Indeed, I spent numerous Saturdays in the 1970s crushed on to the terraces at the Gwladys Street Stand at Goodison Park, the home of Everton FC. Hanging off a rusting stanchion, leading us in song, was a man we all knew as Fozzie Bear. I was never entirely sure why; he never struck me as lovably cuddly or sweetly hapless, like his namesake. On the contrary, he was a denim-jacketed hard knock, and only a fool would cross Fozzie by trying to initiate a chant ahead of him. But his nickname showed how The Muppet Show had permeated 1970s society in Britain: from football terraces to the House of Commons, everybody knew someone who, for one reason or another, reminded them of a Muppet. It didn't even have to be an insult.

It is hard to impress upon children reared on 21st-century reality shows just how large the make-believe Muppets loomed on television in the 1970s and early 1980s. Michael Parkinson still cites a 1978 edition of his chat show, on which the irrepressible Miss Piggy tried to talk him into bed, or at least into showing his legs, as one of his favourites.

Aptly, the man we had to thank for all this was himself a ringer for a Muppet. The television mogul Lew Grade, short, bald and opinionated, would have slotted in perfectly between Statler and Waldorf in their theatre box. Grade was a sucker for puppetry; he had enthusiastically bankrolled the work of Gerry Anderson of Thunderbirds fame. But even Anderson himself recognised that the Thunderbirds puppets were unsophisticated; Lady Penelope was no match for Miss Piggy.

The creator of the Muppets – supposedly so-called because they were part-puppet, part-marionette – was the brilliant puppeteer from the American South Jim Henson, whose marvellous creations, among them the delightful Big Bird, had been appearing on the children's show Sesame Street since 1969. By the mid-1970s, Henson felt that he was becoming typecast as a children's entertainer, and he was right. When he suggested aiming his Muppets at an older audience, the American networks baulked. Happily, Grade saw the potential, and Henson moved his creative team to Britain.

Towards the end of his long life, Grade, a little old man wielding a caber-sized cigar, told me that he considered The Muppet Show and the drama serial Jesus of Nazareth his finest contributions to television. It was a rare impresario who could find room in his portfolio for both John the Baptist and Gonzo the Great. He had recently thought of a way in which another of his puppet series with Anderson, Joe 90, could be revived. "Everything is about genes these days," he said. "So we could inject that young boy with the genes of the strongest man in the world, the greatest surgeon in the world, and do it that way." It was hugely uplifting to find a nonagenarian – Lew 90 – enthusing about the way in which a puppet series about a nine-year-old-boy might be remade for a modern audience.

Sadly, Henson is not around to enjoy the revival. He was only 53 when he died in 1990, and a monumental loss to popular entertainment, not to mention Kermit the Frog, whose voice he supplied. By then, Henson had switched his focus to feature films: The Muppet Movie in 1979, The Great Muppet Caper (1981) and The Muppets Take Manhattan (1984) were all commercial and critical hits, although the first five Muppet films made after Henson's death were less successful.

This latest film, though, called simply The Muppets, reportedly represents a return to the scintillating form of the Henson years and has already grossed over $90m in North America alone, making it the most commercially successful of all the Muppets pictures. Even Statler and Waldorf might find something positive to say about that, but on reflection, hopefully not. In these rapidly and dramatically changing times, when even keeping apace of technology makes your head spin, there is something immensely reassuring about familiarity, and the entertainment world offers nothing more familiar than Waldorf grumbling, Fozzie trying to tell a gag and Miss Piggy getting frisky.

I can see why some folk thought that those might be yesterday's jokes, and that another film might be stretching the Muppet franchise too thin and too far. And yet, gloriously, it seems as though Kermit and co were just what the cinema-going audience was looking for, even if it didn't know it. Moreover, after Kermit's triumphant turn at the National Television Awards, perhaps it won't be long before the fusion of 1976 and 2012 is properly completed. He gave the Best Entertainment Presenter award to Ant and Dec. The least they can do in return is to make him a contestant on I'm a Celebrity – Get Me Out of Here!.