Update...
.. if the neighbour wishes to continue moaning would I be willing to some kind of arbitration... i.e. talk to them and ask what they expect me to do...
..
I'm sorry to say that there is only one thing they want -- no bees. They will not listen to reason, they only focus on themselves.
I've just vacated an Apiary in an Orchard near a "Pick You Own" farm.
For two years it was perfect.
Then neighbour 200yards away discovered there were bees in the orchard and we have had ..
"You should not keep dangerous animals" pointed out that 50's B movies were not documentaries and they had been there for 2 years...
"ouch I've been stung " ( in January with temperatures -1)
"they are swarming in my garden" ( 6 bees on a pitiful waist high weeping willow surrounded by a sea of threadbare grass)
"My daughter was stung, as was 2 of her friends by an angry bee, while eating Ice Cream on the wooden deck " ( a bee with a vivid yellow and black jumper on I guess !)
But after a council call where they told her not to be so stupid, I had some local yobbos throwing bricks at the hives last week and found some empty cans of fly-spray. She's a teacher at a local school................
Fortunately, the yobbos were too cowardly to get close and the bees are calm + working well - the dislodged top supers only creating another entrances, but if I left the hives there I'll probably lose them to anotehr more organised attack.
So be careful your neighbours dont take matters into their own hands.
I think you are only prolonging the inevitable but best of luck and I hope I am wrong.
BTW, anybody know a good site for 3 hives on double brood in the South Bucks area ? ( well no harm in asking !)