This is the key. The prosecutions were all "private prosecutions" by the post office, in which a private entity begins (and sometimes carries through to end) a prosecution _on behalf of the people_.

There is an enormous amount of incredible litigation behaviour by the post office in this case. The problem for them is: it all came to trial in the end and its there for everyone to read in painful detail.

Here is, for example, the post office trying to remove the judge in the case after it all started unraveling:

https://www.bailii.org/ew/cases/EWHC/QB/2019/871.html

And in 929 of https://www.bailii.org/ew/cases/EWHC/QB/2019/3408.html the Judge writes of Post office senior officers refusal to accept to flaws of Horizon even very late in the game:

"This approach by the Post Office has amounted, in reality, to bare assertions and denials that ignore what has actually occurred, at least so far as the witnesses called before me in the Horizon Issues trial are concerned. It amounts to the 21st century equivalent of maintaining that the earth is flat. "