I know Direct Line do this. And in my experience they've been quite competitive on pricing. The idea however behind named driver is that you're not the main driver of the car. Although legally you will be insured and you might not have a problem, it is worth noting that if you did have a major accident, the insurance company would look into more depth regarding how much you have been driving the car. Just thought I'd mention that.
Cheers,
Joe
Joe Burns