AFAIK you can't buy these filters. Only BT can fit them. They're called RF3 filters it seems.
I'm just wondering whether it would be worth you trying an active filter first, something like click here
Have you optimized your internal telephone wiring click here as this could improve your signal to noise ratio and depending on the results, possibly prevent the disconnections.
Other than that, all I can suggest is trying a different router as they are known to produce varying line stats between manufacturers.
I have heard of interference caused by neighbours electrical equipment, but never neighbours ADSL euqipment so this is quite unusual.
Are BT not willing to fit this filter, even though I may be at cost to you?