Nishko,
I had this exact problem a couple of months ago. It's probably worth asking the CAA to fit you into the January sitting, but don't expect too much.
I asked over the phone on the morning my results came out, and was given a flat "no" even though that sitting was nowhere near full. I live quite close to Gatwick so drove over there in the hope of speaking to whoever is in charge of the exams, he too said that there was no way they could let me in for the next sitting. I agree with you that their timing of results and deadlines for exam entry is absolutely ridiculous. Lacks any sort of common sense doesn't it, at a time when students most need any sort of help they can get?
I ended up waiting about 6 or 7 weeks for one re-sit, as it sounds like you may have to do unfortunately. But Capt Crash is correct, there is no reason why you can't start the CPL before you have your results. I did this, although there is a risk that if you fail the exam you will have to put the flying on hold just as you get into the CPL, because I don't think you can do the CPL test until you have passed all the exams. So only do this if, after the exam, you are confident you've passed it.
Good luck with it all,
Billy M