Jim: Yes, that's a known problem in UK, what happens is that if you have uncollected messages with BT Callminder (1571) the next time you use the phone you should hear an "interrupted dialling tone" rather than the usual one. This alerts you to the fact that messages have been left. Unfortunately most modems fail to recognise this tone, and log it as "no dialling tone".
Another problem which occasionaly crops up is if you start using "number withheld" for outgoing calls. With 24/7 type ISP accounts the ISP verifies your log-in details and the originating phone number (stopping you from logging on from several different sites). If your number is being withheld, this cannot be checked, and the system will reject the connection. There is a work-around which involves changing the number dialled for the ISP to start with 1470, which overrides the number withheld status.