Tell your water supplier your move-out date and a forwarding address, plus a meter reading on the day if the property was metered.
If you haven't moved yet and you're on a meter, give your supplier at least five working days' notice so a final reading can be arranged. Leave it later than that and you can end up charged for water used after you'd gone.
Ask when your closing bill will arrive. If you've overpaid, ask whether your account is in credit, how it will be refunded, and when — then chase if that date passes.