What is the phone number for elephant insurance company? The Customer Service Phone Number of Elephant Car Insurance is: (877) 218-7865. Elephant Car Insurance is the providing company of car insurance services. It is a UK based financial services company.What is the phone number for insurance? The customer support phone number of EHealth Insurance is 1-800-299-3116 (Click phone number to call).What is elephant insurance company? Elephant Insurance. Headquartered in Richmond, VA, Elephant Insurance Services, LLC and Elephant Insurance Company are wholly owned subsidiaries of Admiral Group, plc. Elephant believes people who like what they do, do it better and encourages a climate of inpidual contributions, long-term commitment, and profitable growth.