If you use your own car for business journeys, the HMRC approved mileage rates mean that you can claim 40p per mile for the first 10,000 miles p.a. and 25p per mile for anything above 10,000 miles.
However if you carry a passenger on a business journey then you can add another 5p per passenger on to the approved mileage rate. So a drive to see your accountant with three work colleagues will result in a tax deductable payment of 55 pence per mile (40p plus 15p for carrying the passengers).
As with all business mileage claims you should keep a log of the date, mileage and purpose of the business journey (i.e. to see a customer, supplier, bank manager etc). If yo are taking a passenger then remember to note their name on the log in case HMRC want to take a look.