My employer provides protective clothing. Do I have to wash it myself, or should this be my employer's responsibility?

The responsibility for maintenance of protective clothing lies with the employer. Regulation 7(1) of the Personal Protective Equipment at Work Regulations 1992 (note that protective clothing is defined as protective equipment) says: "Every employer shall ensure that any personal protective equipment provided to their employees is maintained (including replaced or cleaned as appropriate) in an efficient state, in efficient working order and in good repair. 

Regulation 8 also requires the employer to provide appropriate accommodation to store the protective equipment when it is not being used. In addition under Regulation 24 of the Workplace (Health, Safety and Welfare) Regulations 1992, the employer is required to provide 'suitable and sufficient facilities' for changing clothes when the person has to wear special clothing for the purposes of work. And finally, the employer must provide the equipment and service it free of charge to the employee. 

So to summarise, the employer has to ensure that the protective clothing is suitable for the nature of the work, protects the employee, and is maintained and cleaned in an appropriate fashion. The best way for the employer to ensure all this is to have control of the process from beginning to end. 

It is also important that you do not take hazards home with you in the form of dusts, chemicals or oils. 

Check your employer's risk assessment and if necessary, seek guidance from a union or legal advisor.