They will not reconsider the SJPN. It is now the only way they have of enforcing the matter.
You have two choices:
You can dispute the charge on the basis that you complied with the requirements of the fixed penalty offer. If you are certain that you did so, as Andy says, a prosecution for the same offence is unlawful. You need to be sure that you did provide your DL details for a second time (i.e. as part of accepting the offer) and ideally have some way to prove that.
Your second option is to plead guilty and when you respond to the SJPN, in the "mitigation" section explain what has happened. Go on to ask the court, respectively, if they would consider sentencing you at the level equivalent to the fixed penalty. Magistrates have guidance that suggest they can consider this where they believe it is just to do so.