Here is the answer you seek:
Find out all of the details of the CCJ - the company who registered it, the amount, court ref number (found on the credit file) account number details, etc.
When you have that, write to the court and contest the CCJ on the basis that your wife did not receive the summons and, therefore, had no way to defend herself. The court will require a fee of around �75 to hear the case.
The case will have to be in your wifes name, not yours.
If succesful in applying for a new hearing, the judgement will be 'set-aside', i.e. removed from your credit file.
At this point, you pay the debt back. The lender will then have no basis for a new case to be heard and the action will be dropped.
You will get a letter of judgement from the court. Send this to experian, equifax who will then remove it from your files.
Works every time !
Then, please be a bit more supportive of your wife. I dont wish to speak out of turn, but to post a question saying your wife is stupid, has f****d up, has annoyed you and that you would consider divorce, just to obtain a clean credit file, is not the words of a loving Husband. You married your wife for richer or poorer and she just made a mistake.
Maybe, if you did not seem so hostile and were a bit more approachable, she might not be getting into these situations and you would solve these issues, however caused, together.
Good luck.