You need to bury a heavy duty wall of plastic between you and the neighbour. I forget the name of it but the rhizomes that keep entering your garden don't go deep (maximum of 2ft) so are easy to stop with it.

What you need is specialist bamboo root barrier - not sure if garden centres sell it, but its certainly available on line. Must be inserted vertically to stop the spread.

Thank you for those suggestions. I had thought that I needed to do something like that, but was praying for a less time consuming/back breaking answer! best I get on with it before it spreads any further. Shame my neighbour didn't do this when planting to save me the hassle.

Jungle Giants sell rhizome barrier. See:

http://www.junglegiants.co.uk/acatalog/Rhizome_cBarrier.html

Another option is to just go along your boundary near the bamboo with a good spade, pushing it about 8 inches down (more if its easy) into the soil.This find any wandering rhizomes. If you feel one, you can just chop it off - but dig out the piece on your side to stop it growing further.
You need to do this for a few feet either side in case the rhizomes are growing out at an angle (they don't just travel straight across the boundary).
If you do this about April and August each year, you should find any rhizomes. (Unless its a Chusquea gigantea, which is deeper.)

Good points: no digging and installing barrier.
Bad points: you have to do it every year that the bamboo is there.

Thanks for that suggestion, will give that a go. Still looks as though I need to take up all my cobbles ( about 4 sq metres ) before I can tackle it. These plants should come with a health warning! My back hasn't recovered yet from jet washing my decks at the weekend and it looks like it will now get even more of a workout.

please update! what did you do and did it work??? *s*