The Yorkshire-born performer made his name singing and playing the guitar in folk clubs and on local radio before featuring on TV programmes including The David Frost Show.
He made more than 1,000 TV appearances during his career and performed in America, Africa, Hong Kong and across Europe.
But he became disillusioned with the business and eventually retired to the south Wales town of Monmouth with his wife Sheila.
He was declared bankrupt two years ago.
Tireless
No cause of death has yet been announced but speaking at the time of his retirement he admitted he had been ill, but dismissed it as "nothing much".
Thackray, who also had three sons, had a string of best-selling albums in the 60s and 70s, and was famous for his more off-beat songs such as La Di Dah and Sister Josephine.
He tirelessly toured but despite his popularity he preferred to play small venues rather than large theatres.
A graduate of Durham University, he went into teaching, first in France and then in Leeds.
Radio success
It was this job that first brought him to prominence after writing songs as a teaching aid for his pupils.
They were featured on the BBC Radio Northcountryman show where they were heard by radio producer Brian Rahey who introduced him to EMI records.
His first album, The Last Will and Testament, featured songs The Cactus, Jumble Sale and Bantam Cock.
Thackray began showcasing his talents on The David Frost Show and Frost in America before appearing alongside Rantzen on consumer champion programme That's Life.
When Thackray retired he said he was "disaffected" with the industry and compared himself to the tragic lead in the film The Entertainer, who kept performing despite limited success.
Family
He said: "I'd never liked the stage much and I was turning into a performing man, a real bloody Archie Rice, so I cancelled gigs and pulled out for a bit."
Thackray's three sons, Bill, Sam and Tom, were at the singer's Monmouth house with their mother and other members of the family.
Bill Thackray said a statement would be made when the family "was ready".