I used to be a 2nd line tech agent for Talktalk and we had simliar stories from customers changing from another ISP to us.
You can change the line profile to a lower noise level to get a more stable line, but this decreases the speed.
An engineer vist to your exchange usually sorts the problem, as we found when the engineer changed the cables from the BT Dslam to the Talktalk Dslam there was a promlem with the cable or connection which introduced noise to the line.
If it is not the cable in the exchange then would turn out to be the drop cable to the customers property, water in the connections corrode the line and introduce noise to the line.
As you live in a flat and share the cable entering the block (ask a neighbour how thier line is), so it could be internal wiring. Does your wire from the distrubtion block run under carpets etc, as they can get damaged from hovers, feet, pets and painting and introduce noise.
If the fault is found in the exchange you won't be charged, if found in your flat you will.
P.S. Always do any line test with a corded phone, as phone companies love to blame cordless phones.