They should be stripped of those powers immediately in my opinion. It's an anachronism and as been shown by this incident they are not fit for purpose.
Private prosecutions are not unusual in England, although the tide may be turning against them. For instance, the RSPCA recently announced that it would stop bringing private prosecutions for animal cruelty [0], which it has done since before there were police. There was apparently pressure from MPs for them to do so, after some fairly high-profile cases where they were seen as being too eager to prosecute.
Of course, the CPS (Crown Prosecution Service) has always had the right to take over and discontinue a private prosecution.
