i had a fault like this
at first my broadband would only work if the phone was off the hook
1st engineer came out and changed my line from the house to the green cab Fixed
then i found my line would drop like yours but only when the phone would ring or be in use
2nd engineer came out did test and said all was fine and walked off as i was trying to explain to him what the problem was
2 month later 3rd engineer came out and asked what the first engineer had done and then said he would be with me in 30 mins
Came to my house and asked me to show him my fault
did the quiet line test and he could see the modem lose connection
He said he would be back in 1 hour
1 hour later he came back and asked me to try it again
All was well and my line stats improved
Asked what he did and he said he changed my line from the green cab to the exchange and said that it was a HR fault
here is a pic of my snr at the time