All my life I have checked the renewal premiums when my car / motorcycle have come due. New customers nearly always get a better deal that loyal existing ones.
In Spain a few years ago I called Linea Directa when I got my renewal as it appeared quite high. I gave a false name but everything else correctly, they quoted 20% than the renew they had sent me. When I told them who I was, they said I was being dishonest by giving a different name. After arguing with them, they offered the renewal with the 20% less. Needless to say, I went elsewhere.