Posted: 25/01/2017 at 15:09
I'm glad I don't live next door to you DHR...
As one who spent a not inconsiderable sum refencing the whole length of our boundary I would be very upset if our neighbours did anything to the fence without approaching me first. I certainly wouldn't just say 'No' if it was a reasonable request - but I would want to know how they were going to go about things.
I have found (also from a lifetime of experience) that if you approach people in a friendly way and explain the problem, explain what you would like to do to make things better and what reasonable steps you will take to not do any damage - then people usually say 'Yes'. They often don't know there was any problem at all.
My suggestion of putting up some free standing trellis in front of the fence means that the OP is doing stuff in their own garden without any need to approach the neighbours. I was sort of reading between the lines in the OP that perhaps there has been some tension around the building of this extension and IMO it never pays to aggravate a fraught situation with neighbours.
Even putting climbers against the fence could cause problems if there are tensions. Stuff like ivy, hydrangea even roses could push through gaps in the fence and eventually damage it.