You may some imbalance in you telephone line, it shouldn't radiate that badly. Having said that the frequency used for your BB is 30KHz and 1.1MHz considering if you are listening to the Brookmans Park Radio 5 Live transmitter which transmits on 908KHz it is within the passband of the BB.
I think its worth having a word with your ISP, whether they will understand I don't know. Do you have a friendly Radio Amateur near you? They are fully aware of these problems and might be able to talk to your ISP on your behalf.