Applying to set aside a judgment (CCJ) is very common for a number of reasons. Firstly, the parking companies realised early that drivers do not always update their change of address details, so they send out claim forms to the old addresses and get a win (CCJ) by default. This means that drivers have to pay £255 court fee for the hearing and may not always win. Applying for a set-aside is very relevant if you work in a job where you cannot have one e.g. banking or where you intend to get a mortgage within 6 years.
One of the problems in asking for a set aside where the Keeper has failed to update the change of address in time is the default position is the last known address (CPR Part 6 - https://www.justice.gov.uk/courts/procedure-rules/civil/rules/part06). Judges can and do refuse a set aside if they feel the Keeper has been lax in updating the DVLA with their new address.
Note: In December 2016, the Ministry of Justice announced they would be looking into this area. They added that "And the Department for Communities and Local Government will be taking further steps in due course to tackle poor practice by private parking companies.
The basis of a set-aside.
To apply for a set-aside in front of a judge, you have to convince the judge of two issues. The first is that there was a good reason why you did not reply to the claim e.g. moved house. The second issue is that you have a reasonable prospect of success.
If the judge at the hearing agrees the two tests have been met, you will get a date for a rehearing at the earliest opportunity. That "earliest opportunity" may be immediately after the set-aside hearing so be prepared for that eventuality by taking all your paperwork with you to the set-aside hearing.