"The process worked lawfully: any flaws were minor and short, and inconsequential."
They also rejected Turner's bid to reduce his 16 year minimum sentence, referring to Turner's lack of remorse, murderous thoughts and the fact the sentencing judge made some allowance for his youth. He was 19 at the time of the murder.
"The evidence does not suggest that the killing was planned in the sense that the appellant had decided he would kill her that night in the precise circumstances in which he did kill her, but it is clear that for some time, because of wounded pride, he entertained murderous thoughts, which culminated in her death.
"[The judge] reflected on all the relevant issues."
"Having examined the ground of appeal, we are satisfied that the appellant was convicted on overwhelming evidence after a fair and proper trial."
"This conviction is safe and the appeal was accordingly dismissed."
The decision means Turner will serve at least 16 years of a life sentence after being found guilty last May of fatally strangling Ms Longley in a jealous, drunken fit of rage.
Ms Longley, who moved to New Zealand when she was 9-years-old, had only recently returned to the United Kingdom before she was killed.
The former Westlake Girls and Takapuna Grammar student was then 17-years-old.
Her separated parents Mark and Caroline Longley made the long-haul flight to London together for the appeal and were present in the public gallery of the courtroom.
Outside court, the pair spoke to media of their relief that the appeal was dismissed - meaning they would not have to sit through the agony of another trial.
"Relieved and delighted," said Mr Longley, when asked for his reaction. "It's two years ago since we saw Emily alive. In those two years Turner's managed to have a huge amount of influence over our lives.
"And that's over now. We can forget about him, remove him from our lives and go on to remember Emily as the bright, fun-loving girl that she was."