BT guilty of harassment and intimidation
Some contributors here seem to have missed the point. Mentioning their good experience with BT doesn't help The Register or those suffering from poor service. There's no balancing force in the universe, and those who experienced poor service are in no way heartened to hear about good experiences.
This is harassment and intimidation, and BT have broken a number of express or implicit terms of their contract. First of all, if not expressly stated in the contract, any court would support the rules of engagement between two entities (rather than an individual) where each party should address a specific department for billing enquiries, and not send a broadcast message to all users.
Next, by sending this message before monies are overdue, BT are not providing an unfetterd and uninterrupted service (that's within within their control).
If my power or water company provided an interrupted service when a bill was due, the regulator would take a dim view. If my landlord shouted a reminder about my bill through my letterbox for all tenants, visitors and neighbours to hear, I could take him to court for harassment.
In BT's favour, I cannot believe that this is corporate policy. There's a nerd somewhere in the basement who thought this would be a good idea because he could do it. However, because of the difficulties in engaging BT and finding the right (or any) warm bodies to deal with this, I'd go straight to Ofcom www.ofcom.org.uk They'll descend on BT like a ton of bricks.