The cost of ordinary commuting is not tax deductible. Ordinary commuting is a journey made to or from home (or any other non-workplace) to a permanent workplace.
A “permanent workplace” is one where either the whole duration of the employment contract is spent; or where more than 40% of work time is spent and the director expects to be there for more than 24 months
The cost of commuting between home and a temporary workplace is allowed, unless the contract comes under the IR35 (disguised employment) rules or the contract is through an employment intermediary such as a Managed Service Company or umbrella company, and the worker is under the supervision, direction, or control of any person.
Aside from commuting, travel for work purposes is tax deductible. When travel is allowable, so are the incidental costs of travel such as accommodation and subsistence.