Usually yes, at least enough to decide if there's something real to answer. You can't just bin it because there's no name on it. Look at how serious and specific it is, whether there's anything you can actually check, and whether staff or the business could be at risk. A vague, throwaway note might need very little. A detailed bullying or safety allegation needs proper attention.
The hard part is being fair to the person it's about when you can't test who said it. So focus on the facts you can verify, not the anonymity, and don't act against anyone on an untested claim. Take it seriously and you're protected. Ignore one that later turns out to be true, and you're in a very hard spot to defend.
Every situation has its own details, and those details change the right answer. For a read on yours, take the free Employee Situation Check or book a call.
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How to handle this, in a couple of minutes
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General guidance to help you decide your next step, not legal advice. Employment law changes, so always check the current position for your own situation.