That's a very interesting question.
Why don't you phone the revenue office that deals with you directly and ask them. If this is a medical necessity I can't imagine that they are that heartless?? It might be that your company puts it through payroll and that you claim it as an expense wholly necessarily and exclusively etc. Though my gut says probably not.
Think on the positives of the petrol money you are saving, and less stress also with time saved using taxi/bus lanes. Will allow you to put your feet up ...... and rest.