It's not really a holdover because the UK allows ANYONE to bring a private prosecution. They just have the resources to do it at scale.

There are legal arguments recounted in modern law textbooks that the whole idea of private prosecutions in England and Wales is a hold-over nowadays. The argument goes that since CPS decisions are subject to judicial review, the raison d'être for private prosecutions, that they allow for bad exercise of public prosecutorial discretion to be corrected by private persons, no longer exists, since the bad exercise of discretion now has another remedy.

There is a fair groundswell of opinion, already driven by the bad reputation that the RSPCA, another prolific private prosecutor, has garnered, against private prosecutions. The Horizon thing only serves to fuel this, and I wouldn't be surprised if there were not soon a proposal to do away with all private prosecutions on the back of these, despite the fact that Post Office Ltd and the RSPCA are institutional private prosecutors, and there's nowhere near as strong a case that personal private prosecutors are a problem.

Stephen Lawrence parents took the option of a private prosecution. Everyone must have access to justice.