Reg Presley died at his home in Hampshire surrounded by his family, his daughter Karen said.
The Troggs had a number of hit songs, including Wild Thing and Love Is All Around, which was covered in the 1990s with huge success by Wet Wet Wet.
Reg 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.
In January 2012, in a letter to fans posted on his band’s website, Reg Presley had 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.”
Reg 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 version, which featured on the soundtrack of the hit film Four Weddings and a Funeral, allowed Reg Presley to pursue his interest in crop circles and UFOs.
Reg Presley published a book, Wild Things They Don’t Tell Us, about the paranormal in 2002.
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