[lawtalkinghuman]

In addition to the RSPCA example, banks/financial institutions bring a fair number of complex fraud prosecutions because it is in their financial interest to prosecute people who've defrauded them. But private prosecutions are indeed an anomaly and can lead to some weird outcomes.

A few years ago, someone brought a crowdfunded private prosecution of Boris Johnson for "misconduct in public office". The whole thing was incredibly silly and a massive waste of time. (MIPO isn't there for politicians lying/misleading people, though that does indeed suck.) https://en.wikipedia.org/wiki/Ball_v_Johnson

Also, following the murder of Stephen Lawrence, the CPS decided to not prosecute for lack of evidence. The Lawrence family brought a private prosecution which failed. Jeopardy attached at that point.

Later evidence emerged which made the case a lot stronger, but had the Criminal Justice Act 2003 not been passed allowing limited exceptions to the double jeopardy rule, it would not have been possible to bring much stronger cases against the perpetrators.

See https://en.wikipedia.org/wiki/Murder_of_Stephen_Lawrence

The CPS have the power to take over and stop an ongoing private prosecution, but the ability to bring private prosecutions sits really uncomfortably with the principle of double jeopardy. Like, someone could do a bad job of bringing a prosecution in a case where the CJA2003 double jeopardy exception doesn't apply and then the person can't be retried by the CPS.