Lee,
Yes you need insurance cover to drive your dad's car. Fully comprehensive cover protects drivers who are named on the insurance policy for any incidents (whether it's their own fault or a third party's). You can ask your dad to add you as a named driver but chances are that the insurance company will not be willing to insure you because you've only got a provisional licence (or the premiums can jump up since you're just a learner).
The best thing to do if you want to practice in your dad's car is to get
car insurance for learner drivers from
Collingwood. This is a special type of insurance designed just for learners. Your dad's insurance will not be affected in any way as the policy will be under your name. If you were to become a named driver on your dad's policy however, any incident that may happen when you're driving will cause him to lose his no claims discount.