HM Revenue and Customs' rules are detailed and complex. However, most expenses paid for costs necessarily incurred during the course of employment will not be taxable unless your employer reimburses more than the actual cost.
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.
Reimbursement of some 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.