I'm already on the electoral roll, do I need to register anywhere else to vote in the European elections?
No.
Apologies - I was wrong. At least it's not quite as clear-cut as I suggested.
If you are a non British EU national then you will have to sign a declaration that you will not be voting in your home country in the European Parliamentary Elections - it's to stop you voting twice.
Voting in Local Government Elections does not require this separate declaration.
If you are affected, ie you are a non British/Irish/Maltese/Cypriot EU national, then your LA should have sent you the appropriate form.
Otherwise all British/Irish/Maltese/Cypriot nationals on the electoral register are entitled to vote in all elections without a separate registration for European elections.
I think it's a recent development as I have never previously heard of a separate declaration for foreign EU nationals. In fact I'm positive it is.
