What can be done to appeal an unjust acquittal?

It was reported this morning that Lissie Harper, the widow of Pc Andrew Harper, has written to the Prime Minister asking for a retrial of her husband’s killers, who at their trial last week were acquitted of murder and convicted of manslaughter. There is also a petition, signed by over 200,000 people, seeking a similar remedy.

I was not present for the evidence at the trial and so cannot offer any sort of valid opinion on the verdicts, but to try to help put the legal issues into context, below is a short thread looking at what the law offers in situations like this.