The CPS have made the decision to charge him and they only do that if there is sufficient evidence for a conviction. I don't know what "perverting the course of justice" means in this case, and I don't think anyone else does, so I'm not sure speculation is helpful.
I assume he is going to plead not guilty and that is why he won't say where the child's body is, as that is tantamount to admitting guilt. He may during the lengthy period of time that he is remanded in custody, change his mind onthat and "go guilty" as they say in court, in which case there would be a possibility that he may say where the body is.
It is unbearable for any of us to think what April went through and the state her parents and close relatives must be in.