no tax to pay on expenses as they should just be reimbursement for things you've had to pay for. things get more complicated if it is a benefit in kind (for example if they contribute to a health plan for you) as that does have a tax implication. your employer will know when this is the case and you will pay tax via payroll and be issued a P11D. sounds like you're not in this league yet.
Travelling to and from your normal place of work are not considered a business expense, so if you firm pays them they would be taxed as a benefit in kind. Travel as part of the job is a legitimate business expense.
I am a teacher in Scotland. If I claim expenses for travelling to a different location (for training etc.) I am taxed on them. Apparently I am a "high earner" as I earn more than �8500 per annum!!