The band are best known for their classic track Ever Fallen in Love (With Someone You Shouldn't've).
Fine Young Cannibals, Pete Yorn and France's Nouvelle Vague are among many other bands to have released cover versions of The Buzzcocks' 1978 hit.
"I am totally shocked and saddened to just hear of the untimely death of Pete Shelley, Glen Matlock who was the bass guitarist for the original lineup of the Sex Pistols, wrote".
On Thursday, the 6th of December, Pete allegedly succumbed to a heart attack while in Estonia where he was living - states the BBC.
Shelley formed the group with original singer Howard Devoto in 1976, and released one of the first independent punk singles, the Spiral Scratch EP, the following year.
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Norman Blake, frontman of Teenage Fanclub, said: "I love (d) Buzzcocks".
"I don't remember the guest house in particular, but it was the beginning of us getting big and we were staying in lots of them, it would have been basic, two to a room, no en-suite toilets".
Thorn called Shelley an "amazing songwriter", while Gaiman tweeted, "part of my youth dies with him". The soundtrack to being a teenager.
"Thank you, Pete, for all the great words and music". The Buzzcocks taught me so much about songwriting, especially in chord structures.
Shelley, whose real name was Peter Campbell McNeish, was born in the English town of Leigh in 1955.