You agree you owe the money. What is the point of trying to get the CCJ set aside? It is unlikely to succeed anyway, because the judge has discretion on whether to grant the request, and it is generally only granted if you can show reasons why the outcome would very likely be different if set aside was granted and the case then re-heard.
My guess would be that the papers - when the claim was originally issued - went to the last known address which the relevant department of the bank had. If so, this satisfied the requirement for valid issue, unless you had already told that dept. of the bank what your new address was. But even if you had, the above para. still applies.
There's no way you can re-open it after you've come to a settlement and paid.