Employees who use their own cycle for work (i.e. not to and from work) are entitled to 20p per mile, tax-free.
If an employer pays less than this, or no cycle mileage rate at all (which is not a good thing, of course!), an employee can still claim tax relief by contacting HMRC (Her Majesty's Revenue and Customs) directly.
For more, see HMRC’s guidance for employees who use their own vehicles for work