Prosecutors in England and Wales are now controlled by the Crown Prosecution Service (CPS) . They will make the decision. The criteria are well know - it is more likely than not to get a convicition and is it in the public interest.
They go into a huddle about this and you as defendant or onlooker have no input ( so it does not become a mini-trial).
Prosecutors do have league tables and do lose their jobs ( which are not elective) if they are bad - but they have to be pretty awful. A 1957 case where a doctor 'got off' when a lot of people think he did it, wrecked the prosecutors career. Allison Saunders had ber contract shortened ( also appointed) ( ie got fired) over rape cases ten years ago, and went to a highly paid job in London. No sad ending there then.
As for the person making the allegations, each case is decided on its facts BUT - a defence lawyer if he knows will exploit the fact they have done it before if a second allegation comes to court
If witnesses patently lie and keep on doing it, there is a category of 'witness crimes'. These are the only crimes they can be accused of. Usually you have to show malice : ( " I knew what I was saying was untrue, but I said it anyway to get him into trouble") - as you can imagine it is VERY incommon for a complainant to confess to something like that.
I have been involved in one of these cases so I know a bit more than Chris ( who is very good). Police going after lying witnesses is very very uncommon - they usually say " sez you - so what?". That could officially be put as " The police show no interest in this whatsoever "