The Buzzcocks, from Manchester, had a string of singles like "Ever Fallen in Love (With Someone You Shouldn't've)," "What Do I Get?" and "Orgasm Addict" and combined a punk ethos with melodies and quirky lyrics.
Shelley, whose real name was Peter McNeish, founded The Buzzcocks with Howard Devoto and they played their first gig in 1976, opening for the Sex Pistols.
He had been living in Estonia with his wife Greta and died there on Thursday, December 6.
The Buzzcocks broke up in the early 1980s but later reunited and remained highly influential to many later musicians.
But what happened to all the other great bands from the punk rock era?
The Sex Pistols
The most famous punk band were the Pistols — originally singer Johnny Rotten, guitarists Glen Matlock and Steve Jones and drummer Paul Cook.
Matlock left the band in 1977, to be replaced by Sid Vicious, who was a fairly inept guitarist but had a public image which fitted in with the band's anarchic and dangerous brand.
The Sex Pistols only made one album — Never Mind The B******s — but their impact on the musical world was huge and several of their songs, including God Save The Queen, Pretty Vacant and Anarchy In The UK, remain iconic.
But the Pistols fell apart after Vicious was arrested in October 1978 for the murder of his girlfriend Nancy Spungen. He was released on bail but died of a heroin overdose in February 1979.
Rotten (John Lydon) formed a new band, Public Image Limited (PiL), and was later accused of "selling out" with appearances on reality show I'm A Celebrity…Get Me Out of Here and TV adverts for butter.
He is now 62 and recently toured with PiL
Jones became a session guitarist and worked with stars including Iggy Pop and Duff McKagan from Guns ‘n' Roses.
In 2014 he appeared as Krull, a road manager for Tim Minchin's character in the US TV series Californication.
Cook, who continues to work as a drummer, married Jeni Cook — a backing singer with Culture Club — and their daughter Hollie is a musician.
When the Sex Pistols broke up at the end of 1978 another London punk band, The Clash, were just getting going.
The original line-up was singer Joe Strummer, guitarist Mick Jones, bass player Paul Simonon and drummer Topper Headon.
In 1979 The Clash brought out the album London Calling — which sold five million copies worldwide — and their sound gradually matured and became more political.
Sandinista! — which came out in 1980 — was inspired by the revolution in Nicaragua.
The Clash broke up in the mid-1980s due to tensions between Strummer — real name John Mellor — and Jones.
Strummer died suddenly in December 2002, aged 50, from a congenital heart defect.
Jones had success in the 1980s with the band Big Audio Dynamite and, now 63, still works as a musician and producer.
Simonon still works in the music industry and is an activist with Greenpeace while Headon was recently diagnosed with hyperkyphosis, a common condition among ageing rock drummers.
The third biggest British punk band were The Stranglers — Hugh Cornwell, Jet Black, Dave Greenfield and Jean-Jacques Burnel — who were formed in 1974 in Surrey and were originally known as The Guildford Stranglers.
The band pumped out hits like No More Heroes, Peaches and Golden Brown as well as politically charged songs like Shah Shah A Go Go — about the Iranian revolution.
Lead singer Hugh Cornwell left in 1990 but the band carried out and will be going on tour in Britain at the end of February.
But Jet Black — born Brian Duffy — will not be with them. He is now 80.
"Jet will do what he can when he can. He's a massive hard worker and he's never shirked away from anything but with the best will in the world you just can't cheat old age," Stranglers guitarist Baz Warne told the Louder Than War website in 2015.
The New York Dolls, who broke up in 1976, are sometimes referred to as the first punk band in the US but that accolade probably belongs to The Ramones.
Many people wrongly assumed the band members — from Queens, New York — were related because they all took on the surname Ramone.
The Ramones' played their last gig in August 1996.
Very sad news— History Of Punk (@history_of_punk) 7 December 2018
Buzzcocks lead singer Pete Shelley has died at 63 of a suspected heart attack.
Their management told the BBC that Shelley died on Thursday in Estonia where he was living.
Rip Pete, you were one of the biggest#RipPeteShelley #peteshelley #buzzcocks pic.twitter.com/iwC5qGQLyZ
Lead singer Joey Ramone (real name Jeff Hyman) died of lymphoma in 2001, aged 49, while bassist Dee Ramone (Douglas Colvin) died of a heroin overdose in 2002.
Guitarist Johnny Ramone (John Cummings) died of prostate cancer, aged 55, in 2004 and the last original member, drummer Tommy Ramone also died of cancer in 2014.
In the 1980s a new wave of punk bands came to the fore — the Dead Kennedys, Black Flag, Green Day, New Model Army, Killing Joke and The Cult.
One of the loudest and fiercest of this new generation was The Exploited, who were formed in 1979 in West Granton, a deprived housing estate in Edinburgh.
Founding member Terry Buchan, was soon replaced by his brother Wattie, a former British Army soldier who sported a prodigious Mohican haircut.
In 1980 the band's album Punk's Not Dead was launched and contained classic punk tunes like Ripper (about the Yorkshire Ripper), Sex & Violence, I Believe In Anarchy and SPG, which was about the notorious police Special Patrol Group.
Peter Hook leads the tributes to Buzzcocks lead singer Pete Shelly, saying: 'Without Pete & the Buzzcocks I would probably still be working at the Docks.' Shelley, who was born in Leigh has died at the age of 63. pic.twitter.com/QYOKZ1smQm— BBC Radio Manchester (@BBCRadioManc) 7 December 2018
The following year the band played Dead Cities on the BBC's primetime show Top of The Pops, no doubt to the bewilderment of terrified parents across the land.
There are numerous anecdotes about The Exploited which largely revolve around drunkenness, violence and vandalism.
The band continued to tour right up recently but Wattie suffered a heart attack on stage in 2014.
Happy Birthday to Walter David Buchan known as Wattie Buchan, Scottish punk rock musician and lead vocalist for the band The Exploited, born on this day in 1957.#punk #punks #punkrock #punksnotdead #staypunk #wattiebuchan #theexploited #history #punkhistory #historyofpunk pic.twitter.com/gAle1WGio4— History Of Punk (@history_of_punk) 24 July 2018
He is now 61 but in August 2018 the band posted an update on his condition on their website.
"Unfortunately Wattie has been having more issues with his heart and faces further surgery. Doctors have advised that he cannot perform any upcoming gigs….We are trying to reschedule for next year sometime. We're really sorry and gutted about having to cancel these shows…and all we can do is apologise," said the statement.