R v Rogers, Tapecrown Ltd, and Beaman  EWCA Crim 801
This was a criminal appeal against sentence where new evidence was sought to be adduced.
The Court of Appeal dealt with the well-established principles governing the admission of fresh evidence at the appeal stage.
Essnetially the new evidence must (a) be capable of belief, (b) afford a ground for allowing the appeal, (c) have been admissible at the lower court, and (d) there must be a reasonable explanation for the failure to adduce the evidence at the lower court. This list is not exhaustive. Interestingly this reflects the rules on fresh evidence in Civil Appeals - see Ladd v Marshall  EWCA Civ 1. In the criminal jurisdiction the admission of fresh evidence is governed by s23 of the Crimianl Appeals Act 1968.
One thing the court did re-iterate was that it can receive further evidence without applying the test where it related to either progress made in prison (especially for young offenders) and information given to the police ('texts').
These rules apply equally to appeals against conviction.