Like much recent legislation, there is not a straight forward answer. You can get a leaflet from the Health and Safety Executive called "Working alone in Safety". In short, your employer has a duty to carry out a risk assessment, identifying hazards of the work, and to put in place measures to avoid or control the risks. They have a legal duty to consult employees on health and safety issues. The control measures may include instruction, training, supervision, protective equipment etc. They should check from time to time that these measures are in place and complied with. You could ask your employer for details of the risk assessment. My guess is that they consider working with dryers and washing machines to be low risk.