According to BT Broadband Help (and they provide the actual broadband service regardless if you go with them, Wanadoo, AOL or whoever) Cordless phones are NOT compatible with having broadband put on a BT line. Something about the frequency of the broadband signal can interfere with the way the base station to cordless phones decodes and transmits the signal to the handset.
Ironically, cheaper cordless phones do tend to work, although you will often notice up to a 35% drop in broadband speed just by picking up the phone. Your model of cordless phone simply isn't compatible; either you will need to use a cheap cordless phone (in which case the results might be unpredictable) or you'll have to use a corded phone. Or you'll have to cease broadband, which I doubt you want to do.