Helen,
Have you tried contacting your current insurance company and ask them whether they'll give you a discount for getting your own policy with them? It is better if you approach the company with which you are insured first to discuss this because other companies will not take into consideration good driving records of named drivers. If you stay with the same company, you've got better chances of a reduction in premiums than going with other one.
I'd say go on car insurance comparison sites and see what is the cheapest quote that you can find. If your current insurer can beat the quote, then you might as well stay with them. Some companies are rewarding named drivers for being claim-free by giving them a discount if you take out a policy in your own name but the discount cannot be transferred to another company if you were a named driver on a policy with them.