What a load of b*****. Quasi-judicial process indeed. It's a statutory process as created by Parliament. And the London Councils have nothing to do with the process.
Anyway you have to wait until the eejits register the debt with the TEC and an Order for Recovery (of unpaid penalty charge) is authorised. That will increase the amount outstanding by £10, the Court registration fee.
You can then submit (file) the Witness Statement that will be attached to the OfR,
or download the form, to the Traffic Enforcement Centre (TEC) at Northampton County Court to the effect that you did not receive the Notice to Owner. Counter-intuitively for the purposes of such forms you are the Respondent and the Council is the Applicant.
The TEC will issue an Order revoking the OfR and cancelling the Charge Cert. The Council will have to re-serve the NTO in order to continue enforcement.
You can then challenge the replacement NTO in the normal manner, if indeed the Council are incompetent enough to serve one, on the grounds that the replacement NTO is served out of time and a procedural impropriety has occurred and probably other reasons. If they reject then you can appeal to the Independent Adjudicator where you will prevail.