If the speed difference is that drastic, & the neighbour is able to get 1Mbps, I'd definitely be thinking along the lines of a poor/noisy line, likely caused by poor extension wiring.
The second link I posted gives info on using the hidden "test socket" behind the faceplate of a standard NTE5 BT Master socket.
Here's another:
http://www.skyuser.co.uk/forum/view-master.html
The test socket bypasses all the extension wiring. If, when using the test socket, things get better, then it suggests that the problem is an internal one - e.g. extension wiring, noise from the ring wire, how the modem/router is connected to the socket, etc.
One potential way of cutting down on noise caused by internal wiring is to
disconnect the "ring wire" from the back of the faceplate (orange/white wire, terminal 3).
Using something such as an I-Plate or a filtered faceplate can also help, if the test socket improves things:
http://www.skyuser.co.uk/forum/cabli...faceplate.html
However, if nothing improves when using the hidden test socket, then it could be that the issue is outside the customer part of the wiring and is an issue for BT (e.g. some sort of actual line fault).