Is personal car insurance effective while driving at work..?

I have personal car insurance coverage for my car, and i have a job that requires some short driving trips on a daily basis from time to time. The company has said that based on my driving history (6pts<3yrs) that they cannot insure me to use a company vehicle, or even drive my own car for company purposes. Does this make sense, doesn't my own insurance allow me to drive me own car regardless? anyway around this?