Setting up utilities at your new address doesn't automatically close your old accounts. Those accounts are between you and each provider, and you need to contact them directly about what still needs doing.
Bill acts only within the authority you've given him. Check your set-up confirmation for the services arranged at your new address.
When you move, the accounts for your previous address to deal with are usually energy, water, council tax, broadband and your TV Licence.
Before you go, check whether any of your current providers charge an exit fee. And don't treat a cancelled Direct Debit as a closed account — you can cancel one through your bank at any time, but the final bill still has to be settled, so tell the provider and arrange payment or a refund with them.