I have a spare (old) modem that I keep just for testing where speeds are decaying or the line is not working. Thus far, from about six tests over three years for various friends, the problem has always been with the wires between the BT exchange and the master socket.
It's a bit of a faff to set up the modem for the different accounts, and to be honest modems usually either work, or don't work. It seems to convince the BT India Helpdesk though, when I say "I've tried a different modem in the master socket".
What I have had to change a few times is the ADSL filter - and I've had new ones fresh from the placcy wrapper turn out to be dud.