The Jagger-Richard song has never really been off the air since then, although its singer has lived through chequered times which have included controversy over his spell of trading in military memorabilia, a serious road accident, a jail sentence for non-payment of rates, and a period in bankruptcy.
Last week he looked back on them with the serenity that comes to the luckier ageing rock stars. "I'm an optimist," he said. "I like to face things and treat them all as part of life. I like adventures - I even went to prison wanting to see what it was like inside."
Now 55 (he was born four days after John Lennon and the day before Cliff Richard), Farlowe retains a loyal following both at home and on the Continent, despite being somewhat bulkier than in his glory days, and continues to perform live and release albums, his gravelly, bluesy voice as distinctive as ever.
He never knows when or where he is going to be recognised. "People are always stopping me and saying 'Hey, your song was on the radio today'," he says.
Once he was sitting in his doctor's waiting-room, and saw the receptionist nudge another woman and reveal his claim to fame. They asked him to give an impromptu rendition of his greatest hit. Never having sung in a busy doctor's surgery before, he politely declined. "So they sang it themselves," he recalls.
"Out of Time", produced by Mick Jagger, was the highlight of what was for him a glittering Sixties.
"It seems like only yesterday," he says. "That year of 1966 was a great one for me - and I've always been knocked out that I had the number one record in the week we won the World Cup."
He still lives amid cluttered splendour in the Islington, north London, terrace house where he's always been - in the flat above his mother's - and is now pleased to combine music with a life in antiques.
"I get a buzz out of talking about a piece of furniture or glass," he says. "I used to be a carpenter and joiner, and I like working with my hands.
"I love polishing, cleaning and repairing stuff - getting hold of something that's a bit worn and tired, and making it really nice."
His shop sells furniture and fittings from the Thirties to the Fifties. Naturally, it is called Out of Time.