The strangest thing is that the City of London is very much like a corporation. A business with policing powers over other businesses...?
PIPCU is new and a little unusual, although there's plenty of precedent for having special police units for complicated crime and they sit next to the Fraud bureau in City police units. It's a bit of an escalation - previously it was local Trading Standards who would handle piracy (e.g. people selling copied DVDs at the local market)
(+) How old? Over 1000 years, its origin is unclear.
http://en.wikipedia.org/wiki/Municipal_corporation
http://www.cityoflondon.gov.uk/about-the-city/who-we-are/Pag...
http://en.wikipedia.org/wiki/Reedy_Creek_Improvement_Distric...