Yes. Your employer can tell you to wear safety equipment (such as gloves, visor, or boots) and if you don't, they are entitled to take disciplinary action, including excluding you from the workplace.
You are required by the Health and Safety at Work Act to:
Of course, any protective equipment or clothing has to be appropriate to the situation. For example, boots must be appropriately used when your feet need to be protected, and they have to be fit for purpose (they don't have to be as comfortable as your slippers, but they shouldn't cause you pain or serious discomfort).
And of course you shouldn't be required to pay for them, although if your employer buys them, they are entitled to keep them when you leave.
There is more information on this issue on the web at the Health and Safety Executive's site, www.hse.gov.uk
Just One More Click: Doggy drama about staying safe online at work.