I drive in the EU regularly in my own private car. Will I need to tell my insurer every time I travel?    

A Green Card will automatically provide you with a guarantee of insurance for a minimum of 15 days. Insurers can also specify that it covers a longer period if this is required, so ask for this if you need it.  

However, at the point at which you renew your motor insurance policy, you will also need to ensure you have a new Green Card for your new policy (even if you are still abroad on the date your original policy expires). If you decide to switch to a new insurer, you will need to request a new Green Card from that insurer as well.