You need to raise a grievance with your manager, yes, and if you are wanting to do it formally it needs to be in writing.
If you have not already done so (although you probably have), you should take a look at the ACAS website as they outline things quite well.
What I would say is that raising a grievance, although it is your right to do so, can certainly rock the boat and make things worse for you in the short term.
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