They have access to the suspect. If the suspect don't understand whether they did it, it should call for a full-scale investigation of the software so at least somebody understands exactly why they are guilty.

In Denmark the police thoroughly investigates cases also when the accused plead guilty.

In a country that has a rule of law, punishment is not negotiation. I do realize that it is up for interpretation for the Anglo system due to its over-commercialized legal system.

They weren't investigated by the police at all. It seems that the post office in england can do their own investigations and prosecutions… the prosecutor wasn't even the same you'd get if you steal from a non-post office.