Can I have car insurance when I am not the registered owner

Currently there's no law which states that you need to be the registered keeper to insure a car. However you will find it really difficult to find car insurance if you're not the registered keeper but want to be the main driver. Most insurance companies will want the registered keeper to be the policyholder (main driver) and you will find that a lot of them will refuse to even quote you if the registered keeper is not listed as the main driver.

To answer your question, the registered keeper can become an additional driver on the car insurance policy but it is very rare to find such a company which will accept this nowadays.