The concept of contesting a COFP is a nullity - you either accept it (you can't), or you don't. If you don't accept the COFP, then it has no bearing on anything else, and it is then open to the police (after the expiration of the 28 day suspended enforcement period) to instigate court proceedings - the same as if they had not issued the COFP.
N.B. The fine will be based on the sentencing guidelines, not the COFP, as explained by Daim456 above.