In Sweden we have an e-billing system where your bills show up as PDFs in your internet bank and then you hit accept or deny (and they go in a queue to pay on either the due date or a date you pick). You can also set it to auto-accept new bills from the same company if you want to emulate how direct debit works (with the added benefit of having a period of time between the bill coming in and the due date to verify the amount is right)

If you want to stick to paper bills, they all have the receiving account number and customer reference number so they can be paid manually via a transfer.

In the UK, larger companies usually allowed a choice of the date the payment went out. (After all, they'd rather not deal with failed payments.)

I keep enough money in my accounts (partly because of this) that I don't really care about it, but I'd be surprised if they don't use the preferred date.