Your contract of employment probably gives your place of employment and the right of the employer to request you attend other locations. There may be conditions which you agreed to at the start of you employment, in the absence of such conditions I would expect you to be paid to travel to other locations, the distance to be from your normal place of employment not your home address.
HMRC accept £0.45p per mile as the total cost, including all aspects, of using your own vehicle for work for limited mileage, I doubt £0.20p per mile even covers the fuel cost for a larger vehicle