We called a few days ago, to try to set up a direct debit from my account. They said that that wasn't possible right now, and that we needed to pay the bill we currently had, and then they'd be able to do it. So, we pay it, wait a few days for it to go through (it's currently paid at the bank), and then call again.
They tell us that we have to pay the next bill before they can set it up.
It seems that there is a teeny, tiny little gap between bills, during which a direct debit can be set up. I used to work in a financial call centre myself, and we were able to set up a direct debit, even with a currently pending bill - we'd just have to warn them that the direct debit would take the next payment, and they'd need to pay the current one another way.