2 inches over hanging roof and gutter

I have a situ where we are attempting to sell and move house and the next door neighbour has threatened a boundary dispute over an overhang of 2 inches of the guttering and the corner of the roof of our conservatory.
The house is ex-local authority and the gardens go off at 80 degree angles - so when we built the extension, we built off at 90 degrees - as you would - up to (and not touching) their wall by asking their permission first and with no objections from them.
Try to imagine our extension as a square and their wall running to left side of it at a "one o clock angle". So our top left corner just overhangs their wall (so to speak).
This was built three years ago!
Now, when we decide to move, this potential dispute has reared it's head.
Would the fact that 3 years has gone by hold any weight that this is a silly excuse to block us moving. Or should we be really concerned - we wanna move! (I'd thought they would be glad to see the back of us!)
Their excuse to us is that they want to build an extension too - using the whole garden width (building off at the 80 degree angle - can you even do that?). So they say they would knock down their wall and then rebuild it double-skinned as their extension wall - so our overhang would prevent that plan. (Surely they can't lay those kind of foundations so close the the boundary)
I'll admit, we haven't exactly been getting on with them over the last two years and they have had petty issues against us with in the past (e.g. environmental noise issues that - after talking to the environmental health office - we were told that they were petty and should be ignored. The Env Health told them to get knotted - in so many words) .
So this feels like another different attempt to get at us.
We are all on speaking terms (but only just!)
Any advice would be greatly appreciated.
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snipped-for-privacy@gmail.com wrote in

I would highly recommend www.gardenlaw.co.uk - go into Forums and then Boundaries.
This group has many, many experts in this field (pardon the pun) and this is a problem that I have seen aired a few times there.
Good Luck
Terry
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Great stuff
took your advice (and got feedback from their forums already)
Thanks
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