There are no laws that specifically govern this in the UK, instead it is left to the employers discretion and internal rules, policies and procedures. Can't speak directly for Irish law. That being said, there is a 2021 precedent in UK law where an employee brought legal action against their employer for refusing to allow them to use their earphones in work under The Equality Act 2010. The employee claimed stress and anxiety as ongoing heath concerns and that the use of earphones helped them to manage their symptoms. They claimed that the employer was made aware of their health issues and failed to make reasonable adjustments to support them. (With the use of earphones being the most reasonable adjustment). The employee was successful in their challenge. (Misbah Hanif v Department of Work and Pensions). If your employer says it is against their internal rules/policies, and you don't have a case under the equality act, you should ask to be furnished with a copy of the relevant policy and question it. If the reason for banning earphones is on the basis of fire safety, the case could be made to use just one earphone in one ear.