If you dial 17070 on your telephone you can check to see if you have a noisy line - listen to the menu options and choose Option Two. It's free by the way.
A noisy line will reduce ISP speeds.
I have a cordless phone, two extensions, an answering machine and the modem in use on my (fairly ancient) BT system without any problems - average speed is 49.3kbps with Tiscali and 52kbps with Pipex on dial up connections.
The only work BT has had to do on my line was about six weeks ago which was due to an earthing problem in their section. It reduced connection speeds dramatically and BT checked my system from the exchange, which included having to disconnect all phones etc during the test.
As a result a BT engineer spent two hours completely rewiring the system from the house box (on the front of my property) to the master socket, running it under the floorboards rather than under the skirting board; he also provided the very latest master socket box and several other useful improvements.
Because the problem originated in BT's section I did not have to pay the £50 plus VAT charge which normally would have been made.