You can approach anyone for a quote - premiums and payment terms will vary from insurer to insurer. I think what your insurance company were trying to tell you (although not very well!) is that the owner of the car (that is the person with the insurable or financial interest) has to insure the car in order for the insurance to be valid. The premium would also have to be rated on your son as the main driver, so unless you've got a spare no claims bonus (from a second car that you no longer have, for instance) there will be no financial benefit in insuring the car in your name.
Unfortunate as it may seem, young, inexperienced drivers tend to have more frequent and expensive accidents and this is why the premiums are higher. It's not worth 'fronting' the policy falsely, because if he does have an accident and the insurance is invalid, the potential costs could be catastrophic!! Hope this helps!