It will depend on why the other claim was not responded to. If there is a possibility that it was mistaken as a duplicate of the other claim, you'd have to convince a judge of that. A single digit difference in the claim number from the same claimant could be an excuse.
The point is, you have already defended a claim by the same claimant, so why would you not defend a second claim. The Overriding Objective is that you would have a reasonable prospect of successfully defending the claim and would have defended it.
The only issue is that it will cost you £303 to apply for the set aside with no guarantee that it would be successful. It would be applied for under CPR 13.3 and there is case law that supports any claim being set aside as part of the Overriding Objective should be granted.
You could ask that the application fee costs be reserved pending the outcome of the claim being successfully defended which means that if you are subsequently successful with your defence, the application fee would be paid by the claimant. They are likely to try and resist because they have done nothing wrong by applying for a default CCJ as the claim was not even acknowledged or defended and they sent all the correspondence to the correct address (as you have stated, you are using your fathers address for service).
There is a possibility that the court would grant the set aside but that the claim has to be defended and they do not award the application fee against the claimant. So, you'd already be £303 down and still having to defend the claim.
Whilst the claim is easily defended and has a very good prospect of being successful, it is not guaranteed. By paying the CCJ in full before 18th December, it will be expunged from the record and that will be the end of it.