Yes, you can reclaim VAT on mileage.  The VAT element of the mileage claim is based on the company car fuel rates. 

The calculation will depend on the engine size of the car and the type of fuel that it uses.  If, for example, you have a petrol car with an engine under 1,400cc, the current fuel rate is 15p/mile.  Of the 45p/mile claim, 15p/mile is for fuel (the rest is for running costs and depreciation) and so VAT of 2.5p/mile can be reclaimed (15p x 1/6).  However, in order to reclaim this amount, you need to have fuel receipts that show at least this much VAT being incurred.