The beginning of the end of Britpop is often dated to August 1997. That was when Oasis’ bloated, “cocaine-addled” (copyright every rock critic ever and Noel Gallagher) third album, Be Here Now was released. It is, despite what Mad Men actor Jon Hamm told The Observer this week, most definitely not a great record.

Those sieving through the tea-leaves of Britpop’s demise might be better directed to the release of the Help! Album in September 1995. where the great and the good of the genre had 24 hours to record something for the Warchild charity. Blur served up a slight piece of whimsical fluff, Eine Kleine Lift Musik. Oasis offered a forgettable song Fade Away with their new mate Johnny Depp on guitar and Kate Moss on vocals. The Manic Street Preachers and Suede delivered cover versions.

Radiohead contributed Lucky.

Whether the British music scene is a sprint or a marathon, this was when the Oxford band broke away from the pack. This searing 4:20 gut punch was a huge step forward from the promising indie guitar band who released The Bends. Their third album OK Computer, from which Lucky was an early calling card, shuffled on to release two years later in 1997.

At a time their musical peers were looking to lift from Revolver, or if they felt really artistically ambitious, Dark Side of the Moon, the template for OK Computer, their first collaboration with producer Nigel Goodrich, was Miles Davis’ improvisational, cussed trip down his own musical rabbit hole, double album Bitches Brew.

Since OK Computer, Radiohead have existed in their own lane. For them and their competition, Britpop very much took up the rear view mirror. By rights, an album like this should have sidelined them commercially into the bracket marked ‘critically acclaimed’. The singalong stadium anthems which went round and round and round were not to their tastes.

It was the start of two decades without compromises – the cover of Q magazine to promote Kid A (a seemingly self-taken photo of the side of singer Thom Yorke’s head) put the band straight in the awkward squad as far as the music press were concerned. Interviews were refused. Two decades of dizzying success followed, including 30 million album sales. These were albums with their own experimental texture, musical tautness and sense of play like Kid A (2000), Amnesiac (2001), Hail to the Thief (2003), In Rainbows (2007) and A Moon Shaped Pool (2016).

Friday night’s Pyramid stage appearance at the Glastonbury Festival was a return to where they appeared in rainier circumstances in 1997, the last year they might have been considered to have musical peers.

At a time other Grammy winners post their own lunch on Instagram, Yorke, Colin and Jonny Greenwoods, Phil Selway and Ed O’Brien are still hard to categorise, hard to read and hard to predict what they’ll produce next. No alarms and no surprises? Their career suggests the opposite.

A rare 2016 “in the studio” piece for the Times Literary supplement attempted to reveal more but writer Adam Thorpe was only given brief glimpses of the recorded process. He found yoghurt cartons (used as an instrument), a hand-built sound machine with added hammers and analogue speakers while outside the group’s resident artist Stanley Donwood tried to fashion what the record sounds like on acrylic canvas. When the Stones made records in the south of France, it was not like this.

Thanks to their mix of dissonant anthems, innovative percussion, Godrich’s distinctive production style (present since 1997) or Yorke’s delicate vocals, the band appeal to rock and classical fans alike. Indeed, guitarist Jonny Greenwood, an exceptional musician by most standards let alone rock star ones, scored two Paul Thomas Anderson films (including the Academy Award-winning There Will Be Blood) and has enjoyed residencies with the Australian Chamber Orchestra and London Contemporary Orchestra.

No other currently working band can boast the breadth of admiration. Fans include the last two James Bonds. Pierce Brosnan was at their O2 gig, Daniel Craig and Sam Mendes asked them to record a song called Spectre, before producers foolishly opted for Sam Smith’s theme. Justin Timberlake says 2000’s Kid A inspired him to embark on a solo career. Prince recorded a version of Creep, as did Tears for Fears and Damien Rice.

The musical theatre’s finest living practitioner, Stephen Sondheim expressed his admiration to Billboard in 2015. “Most pop music’s not about harmony, and for me all music is about harmony. Pop music is ­primarily about rhythm and sound, the combination. But if you ­listen to Jonny Greenwood, it’s about the music as a whole. It isn’t ‘Oh, what a great tune’ or ‘That’s a great rhythmic idea.’ ”

The classical music critic  of the New Yorker Alex Ross is as likely to write about them as the magazine’s pop critic Sasha Frere-Jones. On OK Computer, Ross, the author of The Rest Is Noise which covered the music of the last century, wrote: “Ideas unwind in every register. Paranoid Android is a symphony in six minutes…This band has pulled off one of the great art-pop balancing acts in the history of rock.”

Even more than acts like Sigur Ros, Joanne Newsom and Bjork, Radiohead are the accepted Rock Act It’s OK for Classical Musicians To Like. Ross calls them “the English composers.”

To that end, have a quick flip through the band’s entry on online film encyclopaedia IMDb. To add Radiohead to a soundtrack – even for laughs as the creators of Father Ted did in their last ever episode – is to suggest good taste on the part of the film-makers.

The same track used on Crilly Island, OK Computer’s Exit Music for a Film, was written for the closing credits of Baz Luhrmann’s Romeo and Juliet and has cropped up in various shows from Westworld to Charlie Brooker’s Black Mirror. This led US website The Grinder to call it “the new Hallelujah” in reference to the ubiquitous Leonard Cohen number.
Other Radiohead tracks have cropped up everywhere from Match of the Day, Dancing with the Stars and Twilight to CSI.

Their set on Friday at Worthy Farm – which divided music critics – could have been been either a collection of abstract deep cuts or reasonably big hit singles. The Radiohead faithful, a committed and knowledgeable set of fans, want both and as a result always end up happy – even if the music might not sound that way.

They know by now always to expect plenty of alarms and a few surprises.