Hello, I'm Keith and happy to help you with your question.
I think you are right. Here is the Gov UK preamble on company car tax:
'You’ll pay tax if a company car is given to you or your family to use privately, including for commuting. You pay tax on the value of the company car, which depends on things like how much it would cost to buy and the type of fuel it uses. Its value is reduced if you have the car part-time or you pay something towards its cost. If your employer pays for fuel you use personally and not for your job, you’ll pay tax on this separately.'
Now commuting, which might attract the tax, is the regular use of a vehicle provided by the employer from home to a regular place of duty for your daily employment. The test is consistency of the daily journey. It is abundantly clear that this is not the case here so the application of tax is not incorrect.
The problem is clearly with a rather dense accountant. Just tell him bluntly that if he does not get down to sorting out the mess he has created by his own stupidity you will report his incompetence antics to his professional association, if he has one, That should concentrate his mind and if it does not do not hesitate to report his antics or lack thereof.
I do hope I have shown you a way forward. Needless to say start by being firm, then, if necessary, branch out. Make sure you put everything in writing so there can be no grounds for confusion.