The royal mail had all sorts of powers, historically, as it was a royally sanctioned monopoly, with a charter. The process of privatization left some odd conventions around, such as that it was normal for Post Office Ltd to prosecute things privately, when this has been exceptional for most other entities.
The Post Office used to prosecute for television licence offences, for example, and that only went away relatively recently compared to some of its historic powers. Historically, it had a monopoly over telephones and telegraphy, and some of the powers that the Post Office had in the 19th century were things like compulsory purchase of anyone running private telephone or telegraph systems or prosecuting people for traffic offences on the highway just because there was a mail coach involved.
The Post Office Act 1953 granted the Postmaster General some very sweeping powers, and set the bar quite low for proving fraud against the Post Office: basically, the Postmaster General's say-so for some elements. The Postmaster General also had to give consent to all prosecutions of offences against the Post Office, effectively putting prosecutorial discretion in the hands of the Post Office. And the Postmaster General also had the power to collect the fines upon conviction.
And that's part of how we ended up with the situation at the start of the 21st century.