I have two broadband accounts at different locations, both required to have a fixed IP address. One, provided by Eclipse Internet allowed this by logging on to my account and ticking a check box.
BT have so far:
1. Sent me a new broadband modem (not required).
2. Scheduled a time for the upgrade (a couple of weeks later).
3. Taken the connection down for the entire day to change a non connection specific item, ie. the IP address.