Be careful. Apparently they can only change the direct debit date by moving you onto the Monthly Payment Plan which uses future quarterly estimates for your charges (and going by the many complaints about it on this forum you probably don't want to be on that). Some customers have found this out the hard way and had a lot of hassle getting being put back on the Whole Bill Direct Debit payment method.
I'm on Whole Bill Direct Debit and have asked to move my DD date in the past. I've been told it is not possible on this payment plan and the fixed date is determined by the day of the month your BT services were originally activated. I agree that seems very limited for a modern billing system.