I've been there, done that, and even wrote to the MP. However, I did eventually get it fixed.
It's a long story, but in essence I lived at the end of a 5km line mainly supplied on overhead wires. Being 10 years ago I only managed to get 1-2Mbps at the best of times, but after 4 months of intermittent service I switched to Andrews & Arnold as they were promising to get dodgy lines fixed. After A&A initiated many more Openreach 'engineer' visits I was eventually blessed by a visit of someone who knew what he was doing, and he discovered that in all probability the cable was broken underneath a ploughed field - a thing they apparently call 'Plough Strike' in the trade. He said that such repairs would take a significant amount of time and money, and I should try writing a snotty letter to overlords of Openreach, at that time headed up by none other than Ed Davey.
Of course I got a standard letter back in response saying that he couldn't get involved in such matters, but interestingly within a few short weeks roadworks were set up beside the field, new manholes were excavated, and new wires pulled through and connected. I was stunned when my speed shot up to a heady 3-4Mbps.
The moral of the story is to use people who can apply pressure on your behalf. A&A were (and still are) exceptionally good, and between their equipment and my Syslog files they gave Openreach undisputable evidence that it was their problem to fix. Did Ed Davey do anything? Officially, no, but I can well believe that something was said to someone along the way.
BTW I'm still with A&A to this day, simply because of their customer service and technical support (not that I need it as I've long since moved). Slightly more expensive, granted, but worth every penny as far as I'm concerned.