andrewNZ: This might have been covered, but...
Your bank CANNOT cancel a direct debit.
A direct debit is an agreement between the company (billing party) and you. You have to notify the billing party (usually in writing) that you have revoked the authority.
The revocation won't (can't) happen immediately, the systems are automated and payments are normally planned days in advance.
The agreement should explain all of this and will specify a notice period.
Once you have notified them accordingly and the notice period has passed, they no longer have the legal right to use the direct debit.
If you want total control you need to use automatic payments or pay manually.
I disagree that your bank cannot cancel a direct debit, your bank must do this immediately if you instruct it to! This view is supported by the Banking Ombudsman:
https://bankomb.org.nz/guides-and-cases/quick-guides/payment-systems/direct-debits/
It says on the above page with regard to cancelling a direct debit that:
You can do this at any time, through your bank or the direct debit initiator. The bank must cancel the direct debit when you tell it to do so, but it will also ask you to notify the direct debit initiator. This is a precaution to prevent the initiator unintentionally continuing to send direct debit instructions to your bank.
If you cancel a direct debit authority but keep using the initiator’s services, you will have to pay in some other way. Direct debits are merely a method of collecting payments. Banks are not responsible for the underlying contract between you and the initiator.
Importantly, if your direct debit is from a credit card, the expiry of that credit card does not necessarily remove the direct debit authority, and you may still be charged.
If your bank fails to cancel a direct debit authority and you suffer a direct financial loss as a result, you may be entitled to compensation. This could include a refund for overdraft fees or penalty interest resulting from the unauthorised direct debits.
So, in the example quoted at the start of this thread, the bank did cancel the direct debit when the customer asked it to do so, but warned that the merchant could reinstate it and use another direct debit if they considered they were still legally owed money by the customer.
Therefore, to cover the possibility of the merchant reinstating the direct debit, I think a written instruction to the bank which states that you want it to cancel any direct debits, and any reinstated direct debits from Merchant XYZ, would be effective because the bank must obey your instructions. If your bank won't obey your legal instructions, then you should place your business with another bank!