Yes. Your employer can tell you to wear safety equipment (such as gloves, a visor or boots) and if you don't, they are entitled to take disciplinary action, including excluding you from the workplace.
Your responsibilities are set out in the Health and Safety at Work Act 1974 (HASAWA), which requires you to:
Of course, any protective equipment or clothing must be appropriate for the work you are doing and the environment you are in. 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.
Your employer must:
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