Did you get the quote in writing, or what was in the contract you signed when picking up the car? If they charged you for something extra that wasn't mentioned, you may have a case. What was the exact wording/ breakdown of the charge?
Legally though, they are fully entitled to insist on their own insurance. To be clear, car hire prices generally include the basic insurance, their policy will have an excess that they will strongly encourage you to cover via an expensive add on waiver. You can choose instead to cover that excess with the likes of insurance4carhire.
I have seen on a few of my insurance policies over the years that they specifically exclude cars that are hired by the insured. Did you get confirmation from your insurance company that you could transfer cover to a rented car? Most exclude them because if there are any issues, the rental company will claim heavily for loss of earnings due to any time off the road.