Have you or a neighbour had a new phone line installed? If so BT may have installed a DACS box which splits an existing line in two and results in a maximum speed of 34kbps.
However it's rare to get that, the typical speed is 28.8 and 26 is common.
It is possible that there is some other cause but I run a website where most people use freeserve and they always email me if there is slow down. My advice is to call BT customer services, if their is a DACS box get them to boost the signal which will raise it a little. 28 is now the benchmark for acceptable line.
Also find out the purpose of the other line, if it was a computer connection Oftel guidelines state that BT should not use a DACS box. In fact they are only supposed to use them if there is insuffecient local capacity to install a complete line, that's harder to find out though.