you go thro' the steps here
http://www.emmlegal.com/fraud-prosecution/what-is-a-private-prosecution/
I thought the right had been limited to extinction but apparently that move was defeated and is specifically enshrined in the prosecution of offences act 1985
according to this site
it is used in Fraud and is remarkably efficient !
I guess you are thinking of the Alder hey father saying he wished to b ring a private prosecution for murder against some of the doctors. Complete non starter
The CPS, DPP and AG have powers to stop a private prosecution which was used in the first stephen lawrence case. Duwayne Brooks' evidence was excluded because the was being erm a bit flighty and without that the case was doomed. And so it was taken over by the crown and then immediately dropped
The Law Officers can also enter a nolle prosequi - which stops the case - dead, which was controversially and famously done in the Bodking Adams case 1957. - after his acquittal, the crown said "o lets try again with this one!". Sir Reginald Manningham- Buller ( yup dad of the MI5 head later ) whose nickname was - Sir Reginald Bullying-Manner - called it a day. Later Viscount Dilhorne - yup Duh-learn, that one