Get a new modem....
I too live in Rural(ish) Kent, I was told that my property would never get better than 500k ADSL due to the length of the line (a smidge over 6km). After reading various websites for boosting line speeds, my line now synchs at ~2.8meg.
I removed all of the existing cabling and ran a shielded cat 5 cable from the point where the dropwire comes into the house, twisted two of the pairs together, bought an NTE5 and filtered faceplate, no extensions are run off this socket, the phone is a DECT plugged into the faceplate. I bought a Billion 7700 modem/router and tweak the settings to force the line to synch at ~1db. The line profile is set to 12db and with that I get ~700k, with the forced ~1db I get ~2.8, some days it'll be as low as 1.5meg and the best I have seen is 3.2meg.
My next door neighbour has done none of this and his line speed is less than 500k.
It'll stay up for a few days and then drop, I don't mind having to reset the modem every now and then, it is a small price to pay for a useable speed.
Don't rely on your service provider to give you the best service, do a little bit of research and you can help yourself.