does the bringer of the private prosecution have to pay legal fees of the defendant if it fails?
From the link above it seems like it might sometimes be a nuanced decision:
Earlier this year, Peter Gray, the former partner of Gibson Dunn & Crutcher LPP, received a substantial costs award after Hammersmith Magistrates Court dismissed a private prosecution brought against him and others concerning allegations of human trafficking. District Judge Tan Ikram reportedly described the private prosecution as “wholly improper”. The Judge’s rebuke is a reminder that private prosecutions, which have swung into fashion in recent times, need to be carefully handled.
However, altho' @lecanardnoir successfully defended a private prosecution and was awarded costs, iirc, several years on, these have not been settled fully.
www.quackometer.net/blog/2018/03/totally-without-merit.html