In January 1955, Britain must have felt like it was finally emerging from the second world war: rationing had ended just a few months earlier, and the country had celebrated Christmas by sending Winifred Atwell's pub piano medley Let's Have Another Party to the top of the charts. Sneaking in at No 18, on the gold Brunswick label, Bill Haley & His Comets had a new entry with Rock Around the Clock, a song the band had recorded as a B-side the previous May. By the time Haley's last hit, Don't Knock the Rock, was leaving the Top 20 two years later, the This Is Tomorrow exhibition had taken place, introducing Richard Hamilton and Pop Art to the world, while Haley had the red-hot likes of Little Richard's Long Tall Sally, Elvis Presley's Hound Dog and Fats Domino's Blueberry Hill for chart company. The world looked entirely different, and Rock Around the Clock was largely responsible.

Sixty years to the week after Rock Around the Clock was recorded, Bill Haley isn't often thought of as a firestarter. Elvis, Gene Vincent and Little Richard have their place in the rock pantheon; Rock Around the Clock, though, has the whiff of Happy Days about it. Maybe Jive Bunny and the Mastermixers are to blame, having sent the song back to No 1 in 1989 as part of a medley, like a latter-day Winifred Atwell, squidging it into the Hawaii Five-O theme and Chubby Checker's Let's Twist Again. But in 1955, no one was talking about the rock pantheon. Bill Haley & His Comets had no rivals. They were the first rock'n'roll band, and Rock Around the Clock was the first international rock'n'roll No 1. Whatever the claims of Rocket 88 or Good Rockin' Tonight or Arthur Crudup's That's All Right Mama to be the first rock'n'roll record, Rock Around the Clock was more important because it was the first rock'n'roll record heard by millions of people worldwide. Yet Haley died alone, in the shed at the end of his garden where he lived, in 1981. He was well aware that people thought of him as avuncular and a little embarrassing, the man in the plaid jacket with the kiss curl and the pudgy face. He couldn't understand why he was so overlooked.

That Bill Haley isn't thought of as rock's prime mover is sad and a little ridiculous. Whichever way you slice it, even forgetting Rock Around the Clock, he was at the front of the queue. No one had blended country and R&B on a single before the Comets' Rock the Joint in 1952. No one had scored an American Top 20 hit with anything that could really qualify as rock'n'roll before their single Crazy Man Crazy in 1953. And Rock Around the Clock's international success in 1955 caused rioting in schools and cinemas, and even became the first teen anthem – the film Blackboard Jungle used it as a theme tune and was promptly banned by the American government. It opened the door for modern pop.

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Raised in Michigan, Bill Haley had been playing guitar for a long time before he had a band, at auctions and medicine shows, on local radio as the Ramblin' Yodeler. Eventually he got himself a slot as a DJ in Pennsylvania, where he played the hillbilly he loved and the boogie woogie and R&B that kids in the north seemed to go for. Putting a band together called the Saddlemen, he played high schools and picked up slang like "crazy, man, crazy!" and "hot dog!" This was in the late 1940s. As they incorporated boogie and teen slang into their own sets, the Saddlemen became the Comets – the name was space-age and futuristic.

What made Rock Around the Clock such a huge success? The lyrics, written by 60-year old Max Freedman, are pretty tame ("Put your glad rags on, join me hon, we'll have some fun when the clock strikes one") and repetitive. But then there's the whipcrack snare intro, an announcement – get ready! There are the massed saxophones, the drums high in the mix, and the repetition of the lyrics becomes hypnotic, relentless. Finally there's the guitar solo, like manic morse code, so exciting and impossibly fast. It was played by a trusted session man called Danny Cedrone, who wouldn't live to see its impact – he died after falling down a flight of stairs in the summer of 1954.

Britain held a special place in its heart for Bill Haley. It comes as something of a shock to discover that Shake, Rattle and Roll was a hit for him here before Rock Around the Clock. It reached No 4 a full year before Rock Around the Clock reached No 1, and 18 months before Elvis had his first hit with Heartbreak Hotel. Eighteen months, then as now, is a long time in pop, long enough to make and lose a career.

That fact wasn't lost on Bill Haley. In his later years he grew increasingly bitter that his place in history had begun to slip, and he was no longer regarded as the foremost inventor of rock'n'roll. This was no paranoia on his part – it was made official when the Rock and Roll Hall of Fame opened in 1986, five years after his death, and its 16 initial inductees included Elvis, Little Richard, Chuck Berry, the Everly Brothers, Fats Domino, Jerry Lee Lewis and Buddy Holly – but not Bill Haley.

Why wasn't Haley recognised? His dozen or so hits came in a short space of time, and the only ones still likely to get airplay are Rock Around the Clock, Shake Rattle and Roll and See You Later Alligator. But that was the nature of first wave rock'n'roll, here and gone in a mid-50s flash: Jerry Lee Lewis, in spite of his profile, had just two major hits. Elvis was the exception.

In his last years, Haley would hang out in cafes and bars in the Texas backwater of Harlingen, hoping to be recognised. Sometimes he was. His kiss curl and ready smile may have scuppered his rock credibility, but 60 years ago he caused a social revolution. Bill Haley had the ability to translate hillbilly, boogie woogie and jive speak into something solid that shaped western civilisation in the second half of the 20th century. Rock Around the Clock remains the ur-rock'n'roll record.