I know exactly what suilvenms is saying. We had the exact same problem a couple of years ago and went through the exact same procedures that they did. We kept losing our phone and broadband after every heavy downpour and the problem was identified as being at the green box at the roadside about 3/4 mile away. BT sent underground engineers down to fix the problem but they didn't fix anything.
I spoke to one of my mates, a BT engineer, about it and he showed me a map on his laptop of the underground cabling. The majority of the cabling in this area is aluminium, because copper was too dear in the 70s, and any kind of damp in the underground system messes with lots of wiring.
My mate had a look for me and said that there was only 2 things that could be done.
First, swap us over in the green box to a spare connection - but there was none available.
Second, to swap us over at the telegraph pole with another household. After assuring us that he would try to swap with a house that didn't require the high speed broadband I saw him up the pole the next day. He just gave me the thumbs up and the job took him about 2 minutes.
Our broadband jumped from many disconnects at 400-600kbs to no disconnects at 4.5mbs.
What a difference. I think the only other alternative would be to pay for a new line to go in.