Now the 42-year-old, who has four children of his own, is two weeks into a hunger strike in a Moroccan jail, having become one of a growing number of lorry drivers convicted for drugs smuggling. And according to latest medical reports, he is unlikely to survive beyond Christmas.
Bryant's case is one that has prompted a new joint initiative between UK Customs and the United Road Transport Union. Signed two weeks ago, the "Memorandum of Understanding" attempts to put drivers on a par with postmen, airline pilots and ships' captains in acknowledging that not all drivers are guilty when drugs are found in their charge.
It states: "[They] should not, in the absence of further corroborating evidence, be held responsible or be subjected to prolonged detention simply on the basis of being theoretically in charge of a vehicle and/or load on or in which drugs have been secreted."
Unfortunately for Bryant, from Waltham Forest, north-east London, foreign authorities are yet to be convinced. In March 1993, returning from his third trip to Morocco, Bryant was jailed for 10 years after cannabis was found in his cargo of frozen squid. He has always denied any knowledge of the drugs.
His father, Peter Bryant, 65, says: "He wouldn't do that. He's never been in trouble for anything. That was his third journey to Morocco and every time he had aggravation with customs."
Instead, Bryant found himself in jail in Tangiers, sharing a cell with 43 other inmates. He is now two and a half years into his sentence with no possibility of an early release.
"I last saw him two years ago," says Mr Bryant. "I had to stand behind bars 6ft away and I could only hear half of what he said because everyone was shouting around him. It's terrible conditions - just like a cattle shed. I was shocked." His mother, Sheila, threw herself into campaigning for his release but then contracted cancer. "She worked so hard for his release. I think it was all the worry and stress brought the cancer out," Mr Bryant says.
"We went to see the Moroccan embassy earlier this year and they promised us a phone call from him. But it never came. She was so disappointed." She died in June. The British Consulate said they would "pick the right time to tell him" but Steven, a "mother's boy", took her death particularly badly.
"His kids write to him regularly. But he's very bad, very down. I just don't know what's going to happen to him. I'm at the end of my tether," he says.
According to Steven Jakobi of Fair Trials Abroad, the numbers of truckers convicted of transporting drugs amount to several hundred world-wide. He has approximately 20 such cases on his books, and says that the problem took a "quantum leap" with the breakdown of borders in the European Union.
Mr Jakobi thinks the majority are innocent, and is trying to persuade Brussels' transport commissioner, Neil Kinnock, to make legal changes that would recognise the powerlessness of drivers over their loads.
Fair Trials Abroad has teamed up with the EU's federation of transport workers unions to provide expert evidence in similar cases. They are also pushing for more international memoranda.
But, as Steve Bryant's parents found, getting support for "middle-aged lorry drivers", especially an owner-driver without the back up of a big company, is not easy. "Give me 18-year-old girls and I'll conquer the world," says Mr Jakobi, who handled the cases of Patricia Cahill and Karen Smith, released from a Thai jail after being convicted of drug running. "The problem with middle-aged lorry drivers is simple - they're middle-aged lorry drivers. You can't get publicity."
Meanwhile, the latest report from the Medical Foundation for the Care of Victims and Torture suggested this weekend that Bryant will not live beyond Christmas. In his last letter to his father, two weeks ago, he said that he felt better now that he "could see an end in sight".
"Believe me it is more human to put people to death than force them to live like animals," Bryant wrote. "It is going to be hard for you to accept but I have thought this out and I know I can't handle any more. If you could see how it is here ... then I am sure you will understand."
Gai Kristoffersen, pro-consul at the British Embassy in Morocco, has been visiting Bryant. She disputed that he was depressed and said he was "fine, apart from feeling light-headed" and taking enough liquid.
But she says she has many British prisoners to visit, and many truckers. As for his hunger strike: "The Moroccans haven't really noticed . . . He was accused and found guilty. They won't let him out."
Britons on the route to trouble
John Jones, 55, from Maidstone, Kent: served two years after being arrested in 1992 and charged with cannabis smuggling. He was freed after a royal pardon from the King of Morocco.
John Barber, from North Wales: was arrested in France in 1994 on suspicion of smuggling cannabis and served three months on remand before being released without charge.
Roy Clarke, 48, from Ewell, Surrey: was arrested in Spain in 1994 and charged with smuggling pounds 40m of cannabis. He was acquitted after serving 18 months on remand and being refused bail.
Stan Allsop, 48, from Lichfield, Staffordshire: was arrested in Calais in July, on suspicion of smuggling pounds 8.5m of heroin. spent 10 weeks on remand before being released without charge.Reuse content