HM Revenue and Customs' rules are detailed and complex. There are exemptions, but, in general, expenses are treated as remuneration (i.e. taxed as earnings) unless a specific exemption applies.
Mileage allowance, paid in return for the use of one's own car during the course of employment, may attract taxation above a specified mileage or rate per mile (45p per mile for the first 10,000 miles and 25p per mile after that).
Reimbursement of relocation expenses on moving house as a result of a transfer of employment, above £8,000, may be taxable.
For further advice you should contact your local tax office.