To be exempt, your employer must tell you not to use the vehicle for private journeys and check that you don’t.
You just not using the vehicle for private use is not enough. Your employer must have the policy that it is only for business purposes and no personal use is allowed.
If the car is available to you for private use which could mean you take it home and have access to it then HMRC could still question that.
Your employer's policy is to make the car available and that is why they most likely answered with "that's just the way it is".
That would not be enough. The car cannot be in your possession away form work. You cannot take it home and the policy of business would need to be changed.
Your employer would notify HMRC if they changed.
You are most welcome.A positive rating is appreciated so I get credit for the response.