If a horse drawn carriage is trying to pass a car and the horse becomes uneasy, the owner of the car is required to pull over and if necessary, cover the car.

This is part of the Public Health (Control of Disease) Act 1984, sections 33 and 34: Public Conveyances. The taxi driver has a right to refuse anyone who may have a notifiable disease, or they may elect to transport you and then immediately disinfect their vehicle (unlike a bus driver, who must refuse you altogether)….