I would have thought that if a company decides to use bicycles as a means of transport then they would have a duty of care to employees to make sure that the bikes were safe and regularly maintained, that the riders were trained to cycling proficiency standards, that they had clear rules as to how riders were to behave on the roads, and that insurance was provided.
Employees would have a duty to observe the rules of the road, so for example, if an employee ran down a pensioner whilst cycling at speed on the pavement and injured them, this would clearly be a breach of company rules as well as illegal, so the employee could be disciplined as well as prosecuted and possibly sued individually. The company might also be sued, but might be able to claim that the employee was in clear breach of company rules and should be liable.
The company might also make it a rule that employees were obliged to check their bikes daily and make sure that brakes, light and bell worked and that the bike was in a roadworthy condition, but would be responsible for checking periodically that employees were doing this.