EIM36700 | Deductions from earnings: capital allowances: particular items of plant or machinery: bicycles
From HM Revenue & Customs · Employment Income Manual
Section 80(2) CAA 2001
An employee cannot claim capital allowances for a bicycle.
The only way an employee can get tax relief for using their own bicycle for work is by a deduction for mileage allowance relief (see EIM31330 onwards).