You say it is "at the CCJ stage", do you mean by that they already have a CCJ, or are they applying for one ?
If you already have a CCJ against you, you should have done the CCA letter before it got to court. I would still go ahead and demand it though, then when they fail to provide the details, and they almost certainly can't, apply to have the judgement set-asside on the grounds that you have "ONLY RECENTLY DISCOVERED" that there is no documentary evidence that you ever entered into a credit agreement with Kays.
If they get a warrant of excecution it means they will send the baillifs in, just stick to the normal advice on this forum and DO NOT UNDER ANY CIRCUMSTANCES LET THEM IN, then there's nothing they can do but eventually hand it back to the court, you will still be liable for all the costs though, unless you manage to get the judgement set-asside.
Once you get it set-asside, you're back to square one, and the failure to produce the CCA agreement means they cannot persue you for the debt in court again until such time as they do produce it.
You might even be able to claim your previous payments back, but that depends on how much neck you have
