If a jury concluded that the defendant is guilty, I don't think judicial process reform would help. The fix would require at least public education. Reforming judicial process is hard, but fixing public perception seems way harder.
I've heard part of the problem is that the Post Office were allowed to conduct their own prosecutions. If the public prosecutor (Crown Prosecution Service) would have been involved, they would have asked the Post Office for any material which would have benefited the defence (this would be passed as disclosure). Because the Post Office were "victim" and prosecutor they never did this and the defence didn't get this material.
I have said in the past, only half in jest, that if I were guilty of a crime, I would want a jury trial, but if I were innocent, I would want to be tried by a judge, alone.