It depends if your commute relates to a "permanent" or "temporary workplace". The UK tax office does not accept mileage tax rebates from employees if your claim only relates to commuting to and from a permanent workplace i.e. the place of work you need to attend in order to perform your work duties. This is regardless how far or expensive your commute may be. The reason is you accepted to take on that employment "as is". However, you may be entitled to claim mileage tax relief if you commute to a temporary workplace.Read the definition of permanent and temporary workplace here.
Can I claim a mileage tax rebate for commuting to and from work if I'm employed?