[daddylonglegs]

I think that - in theory - each case is unique and was individually tested at a trial where the evidence was weighed and judgement delivered. For each case lawyers need to prepare a case for appeal. Then the prosecution [1] has an opportunity to assess the case and to decide whether to contest it. If they don't contest the case then the subsequent court hearing (once it happens) should be quick.

The set of people convicted for stealing from the Post Office could include someone who was caught red-handed with an open till, wearing a stripey shirt and a Zorro mask and carrying a large sack with SWAG written on it in bold letters. Obviously this hypothetical thief shouldn't be acquitted with all the innocent people.

IANAL

Since 2010 there have been large cuts to the police, the courts, the pay of barristers and to legal aid [2]. The result is a massive backlog in cases and covid came on top of that. So it currently takes years to get anything done in the British legal system. There is a lot more broken that just this particular piece of software.

[1] I don't know if the response to these appeals is the duty of the Crown Prosecution Service or the Post Office. The costs will ultimately be borne by the public purse in either case, the PO is financially obliterated by it's liabilities.

[2] The system for paying the legal costs of individuals in court in the UK. Very little of it is left now.

Edit: I don't think anyone is still prison for these convictions. Most sentences were for less than three years and the whole process has been dragging on for a long time.