The fact that you are not on the electoral register will significantly impair your ability to obtain credit. Many lenders will decline an application immediately if they cannot locate sufficient electoral register trace (some, if not most, will want to check your previous addresses too).
You should get yourself on the register immediately. However, it may take a couple of months for the credit reference agencies' records to be updated, so there is probably no point repeatedly purchasing your credit score within a short space of time.
Are you using the Credit Expert service? If so, you do get a list of the positive and negative factors which have affected the score. It also allows you to project what your score might be if you made some changes. I'm not sure if electoral register is one of the changes, though.
Unfortunately, there is little you can do in the short term to improve your score. It usually takes time to build up information on your credit file which proves your credit worthiness.