The most basic answer is the police investigate allegations of offences, pass it onto the CPS, (in most cases) who decide how the case is dealt with.
There is no requirement to arrest a person suspected of their involvement in an offence unless certain conditions apply and so any information given by a 'suspect' in a voluntarily interview is sufficient for the police/cps/courts.
Standard procedure. The CPS are lawyers and the police often consult them in the very early stages to see if a) an offence has actually been committed and b) what offence to charge the defendant with.
At my local police station, the CPS officers are in the same building so it's not as ominous as it seems.