1) Have tried several filters.
2) modem in test socket, no phone, still 1M.
3) Will try but 2 tends to rule out my phone.
4) Had similar problems with Orange Live Box for years. They sent replacements - no difference.
A couple of years ago a BT engineer came to my home but couldn't detect noise. He said equipment at the exchange needed resetting, but also stated there could be an intermittent fault on the line. I have had crossed lines at times (people's voices coming over my conversations and strange bleeps). Rural broadband is poor in our area. Still 1M tonignt.
I had very similar problems on our phone about 1992 BB(Before Broadband etc)
Initially BT reckoned everything was OK until I managed to record some of it, one Friday afternoon, whilst talking to the Faults Desk, where the girl was deafened by the noise.
It consisted of-
General noise, frequently deafeningly loud
Crossed connections on incoming calls - simultaneously to other lines
Wrong connections on incoming calls - relatives trying to phone us and well-acquainted with our number
Engineering Test Tones
I was already in contact with senior BT staff about the on-going problems (several months), as ours was a high-priority "Red Card" line (Police Stations, GPs etc).
On hearing the recording and getting confirmation from the stricken Faults staff, the BT Manager arranged an almost immediate transfer from the "Cross Bar system", to the other, "System X", in the exchange, also involving a change of number.
The change-over happened on the Tuesday morning.
A message was left on our Answering Machine, that the transfer had taken place; BUT the New Number was not given.
My lady-wife phoned BT; BUT THE BT STAFF WOULD NOT GIVE HER THE NEW NUMBER!!
(Before CLI, 1707 etc).
Eventually, at her suggestion, the BT staff agreed to phone the New Line and give the New Number to whom-so-ever answered!
Two days later, out of curiosity, I phoned the old, discontinued, number, getting an answer from an obviously irate person, who was "fed up", getting all those nuisance calls; and it had been going on for months!
And BT had initially said that there was "NO FAULT".
=========================
I appreciate that your being on a Rural Exchange, there may not be such a "convenient" solution.