Echoing the point made by onearmedbandit, criminal offences are indeed prosecuted by the State, not by the victim.
At its heart, whether or not the CPS decide to proceed with the case will depend upon whether they feel that it is in the public interest to do so. Whether or not there is any public interest in prosecuting will depend upon a variety of factors, including the gravity of the offence, the past record of the accused, and yes, the wishes of the victim. Also the CPS will take into account whether there is any real prospect of a conviction if the case gets to court. If there still is, notwithstanding the withdrawal of co-operation by the victim (e.g. because of independent witness statements), then there is every possibility that the CPS will decide to prosecute.
I hope that helps!