I do sympathise. I've twice had problems with noise on the line and the subsequent BB speed and stability trouble. The most recent was only a few weeks ago - the record was 259 router resets in a 12 hours. The 'threat' of a call out charge is unnerving - I spent most of my life in telecommunications and still thought twice about calling out a technician even though the noise was normally obvious. To be fair, even though there was no noticeable noise at the time the Openreach technician called, he changed the master socket, on the grounds that these have components which can deteriorate and cause noise. Although there are still times when the line is a little noisy stability has returned to my BB connection which was my primary concern- no resets in the last 15 days. You could try a quiet line test - dial 17070 and select option 2 - from the test jack of the master socket. See click here which gives further useful tips e.g. testing/changing the microfilters.
UK's best mobile network 2016: best 3G, best 4G, best mobile networks revealed