Employers have basic duties concerning the provision and use of personal protective equipment (PPE) at work and this document, explains what you need to do to meet the requirements of the Personal Protective Equipment at Work Regulations 1992 (as amended).
Extracts relevant to cycling:
“PPE is defined in the Regulations as ‘all equipment (including clothing affording protection against the weather) which is intended to be worn or held by a person at work and which protects him against one or more risks to his health or safety’, e.g. safety helmets, gloves, eye protection, high visibility clothing, safety footwear and safety harnesses.”
“Cycle helmets or crash helmets worn by employees on the roads are not covered by the Regulations. Motorcycle helmets are legally required for motorcyclists under road traffic legislation.”
“Because PPE is the last resort after other methods of protection have been considered, it is important that users wear it all the time they are exposed to the risk.”
Note that PPE is considered as the last resort for H&S: the first priorities are to remove the sources of danger.