The song, about First World War soldiers stuck in the trenches during the holiday season, originally featured Jona playing a kazoo, but it was replaced by a Salvation Army band for the official release.
The decision turned the track into a perennial festive favourite in the U.K., but Jona and Dave Robinson, the Stiff Records boss who released the track, are both claiming credit for the idea.
"When I played Stop the Cavalry to Dave Robinson, who founded Stiff, he said it was 'just another antiwar song'. I'd just bought an electronic keyboard - the Poly Moog, as used by Gary Numan - so I went back and beefed up the arrangement, playing the melody on a kazoo," Jona tells Britain's The Guardian newspaper.
"The festive angle came from the line: 'I wish I was at home for Christmas.' My soldier is in the trenches, daydreaming about Christmas dinner with his family," he says.
"When we recorded it properly, I got a Salvation Army brass band to play the kazoo parts and the co-producer, Bob Andrews, suggested adding a tubular bell. That made it even more Christmassy."
However, Dave is adamant it was his idea to include the brass band, and insists Jona argued with him about it.
"I've always loved a Christmas single. I think it was me who suggested the brass band, actually, to make it more Christmassy," he says. "We argued over that too. Jona's a passionate, lovely, talented geezer."