It's the CPS, not the victim, who decide whether to prosecute. If your husband says he now wants to go on, the police should refer the case to the CPS. Depending on the circumstances disclosed the CPS may decide to prosecute. They might decide not to, if they think there is no reasonable chance of a conviction, but that's for them. That your husband changed his mind would be one fact for them to consider, but that depends on the reason for his change of mind. If they thought he was manifestly unreliable as a witness and the matter not serious in itself then, clearly, they might not go on. But it is quite common for victims to do this, for any number of good or natural reasons, and the CPS would not be swayed by the mere fact of a change of mind. After all, in this case it appears that the suspect made an admission, which helps.