After suffering from Rein for almost 2 years in 2007 in Bradley Stoke, we (Paul Hucklbridge fro OR and myself) eventually found the cause to be a tripler in a portable television half a mile away. It was wiping out 100% of the signal for >1000 people. So don't automatically think it's your neighbours, anywhere along the line will kill it.
To find it nice and quick (yes, we had another occurence about a year later, this was a bad telephone answering machine wall-wart), found this one in an hour. You really need to get the AM radio out, you have to pick a frequency (I found around 600Khz to be good) that gets a nice loud buzz when you get the rein issue. Stick the radio right next to the phone socket. Make sure it vanishes completely when rein stops.
Then I'm afraid to you need to trawl ebay. Your after an ADF, mines a Nova-tech 'Nova-Pal'. I paid about 20 quid for it. Dial in the same frequency to this as your am radio. Next time the rein hits, power it on and get your shoes on. Turn the gain up full and start walking in the direction of the highest signal, then back the gain off until you find the exact source. I could trace it to within a meter, but you can usually narrow it down to one or two houses in about 10 minutes. Then be polite to the occupents! You need to work with them, usually they are suffering from issues themselves.
Incidently using a normal AM radio to do this is useless as they all have agc, you can spend years walking on top of phone lines and get nowhere (I did!).
Good Luck!
Tim
Here is a google link to a picture of the unit I have:
http://www.google.co.uk/imgres?imgurl=http://pmimage...