Tim,
It is not uncommon for car insurance to go up when you have passed your driving test. When you're a learner, there is always someone with you when you're driving and you will tend to obey the speed limits and motoring signs. However when learners have passed their tests, they tend to be less careful and are more involved in accidents. Hence the risk is greater and the premiums reflect that.
However, I did not fully understand what you meant when you said you will be getting your 1st year no claims discount. Have you had insurance in your own name whilst having your
provisional licence and was not on somebody else's policy? If that's the case, then you can change insurance companies and you will be able to use your no claims bonus to get really good deals.