Unfortunately, without the additional information requested in my first/previous response, I will not be able to give you detailed advice to your question, but I will be able to give you a general answer, which I hope will be of assistance. If you are able to supply the additional information later, please do so and I will then come back to you with a more detailed answer.
Silly as it sounds, and I am sure you have already done so, check the door pockets of the car and under the seats incase it fell of the dash / mirror.
If your car was left unlocked and someone has entered the car and stolen your badge, then report the theft to the police so that you obtain a crime reference number.
Then contact your local authority who issued the badge and report it stolen from your car. They will then arrange for a replacement to be sent to you.
I hope this helps answer your question.
Thank you for using Just Answer and for allowing me to assist you with your legal enquiry. I am pleased I was able to be of assistance. Please do not hesitate to come back to me for further advice on this or any other legal matter. It will be my pleasure to be able to assist you again.