Yes, it is called Mileage Allowance Relief (MAR). If, say, you pay 40p a mile (up to 10,000 miles in a year), that is 5p per mile less than HMRC accepts under the exemption, so your employee can claim tax relief on 5p per mile. You can, in fact, arrange to claim the tax relief on behalf of the employees using the Mileage Allowance Relief Optional Reporting Scheme (MARORS) by reporting the details to your tax office. See http://www.hmrc.gov.uk/paye/exb/a-z/m/m ... penses.htm
. Otherwise, there are a number of ways your employees can claim the tax relief personally, including form P87. See http://www.hmrc.gov.uk/incometax/how-to-get.htm
There is an equivalent NICs exemption for mileage allowance payments - the main difference being that it must be assessed each earnings period - but there is no equivalent to MAR. In the 40p example above, there is no provision for offsetting the 5p per mile against NICs liabilities.