The Troggs had a number of hit songs, including Wild Thing and Love Is All Around, which was covered in the 90s with huge success by Wet Wet Wet.
Presley had announced his retirement from music a year ago after being taken ill during a concert in Germany and being diagnosed with lung cancer.
Music publicist Keith Altham said on Facebook his "dear old pal" had died after "a succession of recent strokes and a losing battle with cancer".
BBC 6 Music presenter Marc Riley paid tribute to the "great character" of Presley. "He was so engaging and, at the same time, having been so influential, he was so humble and so likeable," he said.
In January 2012, in a letter to fans posted on his band's website, Presley said: "As you all know I was taken ill whilst doing a gig in Germany in December. During my stay in hospital tests showed that in fact I have lung cancer."I am receiving chemotherapy treatment and at the moment not feeling too bad. "However I've had to call time on The Troggs and retire. I would like to take this opportunity to thank you all for the cards and calls and for your love, loyalty and support over the years."
Presley was born in Andover, Hampshire, and founded The Troggs in the early 1960s.
The band's other hits included With A Girl Like You and I Can't Control Myself. The 1967 hit Love Is All Around became a hit song again 27 years later when a cover version by Scottish band Wet Wet Wet remained at number one in the UK for 15 weeks. The success of the Wet Wet Wet single, which featured on the soundtrack of the hit film Four Weddings and a Funeral, allowed Presley to pursue his interest in crop circles and UFOs.
The singer published a book, Wild Things They Don't Tell Us, about the paranormal in 2002. Alan Clayson, who wrote biography The Troggs: Rock's Wild Things told the BBC Presley was a "local hero", describing him as a "world expert on crop circles" with an "intelligence within". "I must admit since I knew him I became a great deal less cynical about that," said Clayson. "Reading his book, it's got an intellectual depth of a University professor rather than a former brick-layer from Andover."