Most employers will at some point have to confront allegations of bullying at work. Putting procedures in place as well as managing difficult conversations with the individuals involved is beneficial, not just in the short-term by resolving conflicts, but also by helping create a more harmonious workplace.
Employers can be hit by serious financial, legal and reputational issues if they fail to deal properly with allegations of bullying, from discrimination claims under the Equality Act (if related to a protected characteristic such as sex or age) to claims for breach of contract, constructive dismissal and negligence (if the bullying has caused a psychiatric injury to the individual).