Sprinter Dorothy won the coveted award in 1963 which she had to hand back the following year.
She was given a commemorative plaque, which she still has.
This was before the broadcaster handed out replicas of the main trophy, based on a camera, to winners as it currently does.
But the Chronicle understands the BBC is looking into a replica for Olympic and Commonwealth medallist Dorothy, after she said how much she loved them.
Dorothy said: “When I got it, things were different then. We were in a theatre and it was only an invited audience.
“You got the main trophy and kept it for a year. You were also given a plaque to say you had won it, which I still have.
“Over the years, they started giving out replicas of the trophy which are lovely. I always thought I wished I’d got one when I won it. I just happened to casually mention that I would have loved one.
“I don’t think people realise that I did win it, they always ask to see the trophy and I tell them I haven’t got one.
“But it’s not that they omitted to give me one, they just didn’t do it back then.
“It’s something that’s come in over the years.”
Dorothy still attends the awards evening with her niece, and will do so again this year when the ceremony is in Birmingham. She said even though it was 55 years since she won the award, people still recognise her.
“Last year Gabby Logan walked past and I said ‘you probably won’t know who I am, but I’m Dorothy Hyman’ and she said ‘of course we know who you are Dorothy.’
“Katharine Merry said the same. You think people have forgotten but they haven’t. And of course, I do get recognised in Barnsley which I think is lovely. It really makes my day. I thought when I finished running that after two years no one would remember me, but it’s amazing how many people do.”
Dorothy was just 17 when she went to her first international event, the 1958 Commonwealth Games in Cardiff, where she helped England to win gold in the 110-yard relay.
She burst onto the world stage at the 1960 Olympics in Rome and returned with 100m silver and 200m bronze.
She won a medal of every colour at the European Championships in Belgrade in 1962, and then two golds in the Commonwealths in Australia.
She then went unbeaten throughout 1963, setting world and European records and winning BBC Sports Personality of the Year.
After winning bronze in the 1964 Tokyo Olympics, Dorothy retired from athletics aged 23.
She was presented with the Special Award at this year’s Proud of Barnsley awards ceremony.
Barnsley East MP Stephanie Peacock has also written to Tony Hall, director general of the BBC, to request a trophy for Dorothy.
She said: “Dorothy is an accomplished athlete, Olympic and Commonwealth medal winner, record holder, and Barnsley hero.
“From her childhood in Cudworth to a national household name, Dorothy was rightly recognised for her achievements with the 1963 BBC Sports Personality of the Year award. But unlike other winners, she was not given a trophy to keep.
“I hope our campaign can redress this injustice, bring a trophy back to Barnsley, and give a true champion of our community the trophy she richly deserves.”