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.
HMRC has said that you can claim tax relief on £6 a week of earnings (April 2020) without providing evidence of the extra costs you have incurred working from home. If you want to claim more than this, you will need evidence, such as receipts, bills or contracts. You can only claim for things to do with your work, for example, business telephone calls or the extra cost of gas and electricity for your work area.
Basic rate tax payers who claim tax relief on £6 a week will get £1.20 a week of tax relief (20% of £6).
You can only claim if you are required to work from home (for example during the coronavirus pandemic) not because you choose to do so.