Not if you want to keep it from being a company car (irrespective of the fact that it is personally owned), you can claim mileage though (45p for first 10,000 miles, 25p thereafter)
As Rob states, use the mileage allowance. If VAT registered you can reclaim the VAT on the fuel element only (need to find out the engine size and fuel type) see www.hmrc.gov.uk/cars/advisory_fuel_current.htm
Ensure all fuel receipts are maintained.
But you need sufficient fuel receipts to at least cover the VAT element of the mileage claimed so you do need to keep the receipts if you are going to claim the VAT element of the mileage even though its not a direct correlation between the two and the VAT recalimed will be less than that from the receipts.
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Shaun
Responses are not meant as a substitute for professional advice. Answers are intended as outline only the advice of a qualified professional with access to all relevant information should be sought before acting on any response given.