Caz,
This is the problem for driving as a named driver - you don't get any no claims bonus (NCB) when you set out to get your own insurance policy although you've never made a claim. However a few insurance companies have started named driver insurance which entitles the named driver to get a discount similar to no claims discount (NCD) earned by policyholders when they decide to take car insurance in their own name. You should contact your current insurer and see if you're entitled to any discounts. Mind you that the discount is applicable only if you stay with the same company so if you move to another insurance company, then the named driver discount will not be transferrable. Unfortunately, I cannot say which insurance company can give you cheaper quotes because car insurance depends on a lot of factors like which car you're driving, where you keep the car etc and it's best if you use a car insurance comparison site to see where you can get the cheapest quote.