Note that it is probably a "Direct Debit" rather than a "Standing Order". Apart from other differences, Direct Debits payments can vary in value month to month, but a Standing Order has fixed value payments.
At signup time you should have been offered choices of payment method, with reasons for each choice.
I can't recall all of the choices but one is to use direct debit for all payments (ie no credit card payments), in which case only your Bank Account details would be required.
However, you would have to wait for the Direct Debit authorisation to be processed before your new account can be started. So, to allow your account to be opened without that initial delay, Plusnet offer to take your first monthly payment immediately by Credit Card (as that can be authorised immediately) with all the following payments to be taken using the Direct Debit.
In that case, both the Credit Card and Bank Account details are required.
However, now that you are up and running, I believe you could ask to have the credit card details removed and just leave the direct debit instruction, as this is what I did.
