when you are using a dialup modem the phoneline becomes engaged. I think there are tools which will notify you that someone is trying to call, but I cant remember where to find those.
If you have BT 1571 then if you get a call while online it will be diverted to that, but as that creates a false dialtone, you will be unable to dialout either by phone or modem until those messages have been checked.
The telephone not ringing and causing the modem to disconnect could be a result of not enough power being availble on the line, you might want to get BT to check that.