I'm not sure 100% how this pans out in the Civil Courts, and forums like
http://forums.pepipoo.com/ and
https://forums.moneysavingexpert.com/ca ... es-parking might offer good advice.
In a Criminal Court i.e. speeding fine, a similar case would be dealt with via the 'Statutory Declaration' process, where an individual goes to court to swear under oath that they hadn't received any information via the post. It's not an uncommon event.
Providing the applicant informs the court within 21 days of being made aware of the fine/CCJs/points etc the court will hear the application, although under certain circumstances the court will agree to an extension. If agreed by the court this declaration will cancel any fine/CCJs/points etc and will restart the process from the beginning.
Moving home is the usual reason why people don't get the info, but the court may well ask if the applicant informed the DVLA in good time, as we all should when we move, as CCJs like the one you describe have arisen via info gained from the DVLA.