Car tax is an allowable expense, but you need to work out how much of your car usage is for business purposes. It can be an estimation, for example 60% of the time you drive for business and 40% you drive for non-business related activities. As you are only allowed to claim for business related expenses, in the example above, you would be able to claim 60% of the cost of your car tax.
You are not allowed to claim petrol for journeys to and from work, but any other business related journeys you can claim for petrol. Like if you drove from London to Scotland to pick up a manicure table (just as an example!) then that is fine.
All of this assumes you are self-employed and a sole trader and not a limited company.
Oh, and I'm an accountant part-time and a beauty therapist part-time, so please ask if I haven't made myself clear or you have any other questions.
Lucy x