Looks like Bind weed. It is a pretty white flower but strangles everything else it climbs/binds round. I'd cut it back as far as I could then in the back end of the year I'd spray it with glyphosphate in the hope of killing it over winter. it may take many applications to get rid of it but if the roots are next door you will have trouble getting rid.

I have a constant battle with next door's bindweed. It grows quickly and can start to strangle plants if you don't keep a beady eye out. Fortunately I have access to next door's garden so I spray any bindweed I find that's near to my fence in the hope of keeping it out! There always seems to be some that I miss though....

i have been struggling with bindweed for 3 years, it is in both of my neighbours gardens and the back alley way all coming from a garden a few houses up, but i just pull it out when it comes up can be quite satisfying when there is alot of it that comes up with one pull!!!

thank you for the feedback. i dont think its bindweed, the stems are more woody, it nearly looks like a kind of honeysuckle kind of thing. (although I have to say there is bindweed at the back of the photo. ) any other ideas ? I'll try and take some more photo's maybe.

I think that it is a russian Vine, a real thug. The only thing that you can do is keep cutting it back on your side.

Looking at the photo in your later question - yes, Russian Vine and just keep hacking back!