In the event of an appeal in this case, if the Court of Appeal admits new evidence from the defence - which it might not do, even if the CCRC thinks it does and refers it on this basis - the new evidence would need to make the conviction being unsafe!
Just because there is new evidence which is admissible, that doesn't necessarily mean the conviction is unsafe. The Court of Appeal said this a recent case (R v Norris)!
From the Criminal Appeal Act 1968:
"(1)Subject to the provisions of this Act, the Court of Appeal—
(a)shall allow an appeal against conviction if they think that the conviction is unsafe; and
(b)shall dismiss such an appeal in any other case."
The Aga burns
Take the Aga burns as an example: we are told that this is evidence that the police moved the body because: (a) Boyce says the burns were caused by the Aga (b) the only explanation of Nevill being precariously over a stool is that the police moved him.
Neither of these (a) and (b) are by any means certain. Boyce may be wrong, but even if he is right, why is (b) so?
But even if (a) and (b) are both true, how on earth does this make the conviction safe?
The position of Nevill was not part of the prosecution case (or certainly not a main part of the prosecution case). The main part of the prosecution case was the silencer, along with Mugford's testimony and other reasons put before the jury (e.g. clean hands and feet) which suggested it wasn't Sheila.