Yes, but the distinction here is not actually as useful here as you might think.
In this situation, Royal Mail _are_ the police (the USPS has its own police too). But Royal Mail are also the prosecutors in court (they have/had prosecutorial power).
They didn't really delay sending it to the police because they never would have. It wasn't a police matter because definitively it was a Royal Mail matter. (The Royal Mail has had the power to investigate and prosecute since before there even were police.)
Edit to add: it is now a "Post Office" matter as well because they are distinct businesses as of 2013, and Post Office Ltd is an ordinary company. But the key period concerns a time when they were one and the same