Just spent 40 minutes with Apple support going through this problem having unsuccessfully tried the various fixes stated above. In this order:
1. Ensure the phone is not plugged into the charger
2. Select Airplane mode ON
3. In Bluetooth, "forget' your car
4. Turn Bluetooth off
5. Re-boot your phone by pressing the home button and the on/off button together for at least 10 seconds or until you see the Apple logo (I believe iPhone 5&6 don't display the apple logo?).
6. Depending on model your phone will restart almost immediately, if not use the on/off button to restart the phone
7. Turn airplane mode OFF
8. Turn Bluetooth on
9. Re-pair your phone with your car
If this doesn't work, please call Apple support (excellent chat facility on-line), but it worked for me.