Getting this together before you start saves you a second phone call.
You'll need your account or customer reference number for each provider if you have one — usually at the top of a bill, or in your online account.
If you're moving, have your move-out date and a forwarding address ready too. For energy and metered water, you'll also need a meter reading taken on the day you leave, if you can reach the meter safely.
Already moved without one? Say so. Your provider may estimate the final reading instead — ask what figure they've used, and challenge it if it looks high.