I'm afraid so Lookout. I think the case is political.
You mean due to the impact a successful appeal could have on confidence in the judiciary?
To be honest, I personally doubt that. Unless some startling new evidence comes to light, or there is a radical shift in the interpretation of existing evidence, I think allowing the appeal could easily just be spun as a 'reasonable doubt' case - in effect, just 'one of those things' - rather than a major embarrassment to the judiciary. Any damage to public confidence in the system would be thereby minimised, and it would all quickly blow over and be forgotten in the public mind. It is true that the British judiciary are notoriously poor at institutional introspection, humility and self-reflection, but what I have just outlined is their typical method of dealing with mistakes that can't be hidden any longer: brush it under the carpet.
I think the basic problem Jeremy has is that the case against him was weak, but so is the case in his defence. This is perhaps a unique criminal case, in that regard. The crime scene is an inscrutable black box. There was never one thing that, as such, proved Jeremy was guilty, and he shouldn't have been convicted; but, he was convicted, and so the burden shifts to him, and that has exposed the correlative problem that there isn't one thing, as such, that proves him innocent - though there is scope for reasonable doubt, so it becomes a matter of whether judges are willing to recognise this and exercise their discretion in Jeremy's favour.
Realistically, I doubt appeal judges spend hours looking through case papers, and we know they're not on discussion forums like this. They come to cases fresh and naive about the underlying fact matrix and agendas involved, and (assuming there is a third appeal) this case will be one of maybe a dozen appeals they hear at any one time. The judges will place heavy reliance on what the parties tell them and won't develop a deeper understanding of the case.
Maybe in rare cases such as this, the whole thing should be placed under the supervision of 'examining judges' who investigate the case thoroughly over several years in the manner of a lengthy public inquiry and come to in-depth conclusions and make wider general recommendations about useful reforms to the system. But that would be an expensive system to run and it would also require the sort of institutional introspection that the British judiciary notoriously struggles with.
A realistic way to resolve the Bamber case would be to simply release him on the basis that he has served the time. The problem with that solution is that it doesn't suit either party. People like Steve will jump up and down screaming and shouting that you can't release a mass murderer, even if he's 90 and walking with a zimmer frame. Meanwhile, Jeremy may not want to be released as a convicted mass murderer, and given that he would be a convicted child killer, there will be expensive security measures needed.