AMAPs

AMAPs, an abbreviation for Approved Mileage Allowance Payments 

Reimbursed 45p per mile for first 10,000 business miles and 25p for each mile over the 10,000 mark. Works by reducing the employees taxable pay. As long as the AMAP limit is not exceeded, it will not be subject to taxation.

For employees who have use of their own vehicle – or grey fleet only. 

You can find out more information on this rate at the HMRC's Travel - mileage and fuel rates and allowances page

Your company may pay an alternative rate to AMAPs, under the same principles, where you're reimbursed (x) pence per mile, for the first (x) miles, then (x) pence per mile thereafter. If this is the case, you may be eligible to make a P87 claim at the end of the tax year