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:
Protective equipment or clothing must be used when you are in a risk-intense environment and need to be protected. Of course any protective gear has to fit, and be appropriate for the situation. It shouldn't cause you pain or serious discomfort. If it does, you should negotiate alternative equipment or arrangements. Don't be put off. Sometimes employers can, out of caution, interpret health and safety rules too rigidly.
And of course you shouldn't be required to pay for protective equipment or clothing that you need. However, if your employer buys the gear they are entitled to keep it when you leave.
There is more information on this issue on the web at the Health and Safety Executive's website.
You should also consider raising the issue with your union health and safety rep, if you have one.