The problem here, is that English law distinguishes between wrongful conviction and miscarriage of justice. They are separate concepts. Ellis was not wrongfully convicted, but arguably wrongly sentenced.
No, she was accused of murder, found guilty and sentenced for it. Even today, if she had been tried for murder, she had a useless barrister, who failed to use the diminished responsibility defence, and the jury found her guilty, the judge would have had to follow sentencing guidelines for murder - which would iirc, be a mandatory life sentence. Judges don’t have discretion.
There are two parts to a crime - actus reus and mens rea. I question whether she had mens rea? I suspect she was half out of her mind, given her history and not responsible for what she was doing. Someone else gave her the gun, and showed her how to use it. Imo, he knew her state of mind, and he used her, to take the rap.
A friend of ours is a judge. He tells us, if we were ever to be accused of a crime like murder, keep silent and never confess. A good barrister can argue it down to manslaughter. They can’t, if you have confessed.