He also claims that the hedge now forms the boundary, rather than the pre-existing fence, and that that places additional obligations on us. Anyone know if that is true?
Absolute nonsense!
You can put whatever plants you like in your garden, wherever you want to put them.
Planting a line of shrubs and letting them grow together so as to form a single, continuous, group that some people call a hedge is not moving the boundary. Would they have said the same if you'd put a line of shrubs down the middle of your garden?
You could solve the problem by removing every third plant, or carefully pruning them into groups of two! The high hedges legislation, for example, only refers to groups of two or more evergreens! Deciduous hedges were not included in this legislation because the leaf cover doesn't last for a full year.
As far as I know there is no legislation setting a maximum height for deciduous hedges (ours are probably about 15ft high, all of them are, they were that height when we each moved in and they've stayed that way) and indeed, some people are quite able to get round restrictions for 1metre maximum fence height close to a highway by planting a hedge just inside the fence and letting it grow taller. In that instance there is no question of the council grabbing the land between the fence and rootline of the inner hedge, calling it there own!
There may be local covenants which would be within your title - check carefully.
You do not have to comply with conditions set by your neighbour's insurers, unless it is proved that your actions have damaged their property. Your own insurance should have public liability cover, and probably legal cover - but this is not retrospective and there's usually a delay of weeks or months to ensure people don't suddenly try to insure for something that's already happening. Possibly a good idea to speak to your insurers, just to be sure, in case next door tries to escalate things.
The difficult to answer question is where is the boundary?
Normally the outside edge of any hard fence, but there's nothing to say that the fence has to be on the actual boundary, it could be inside it.
That's muddying the waters. The acknowledged boundary between these properties appears to have been the fence line until the shrubs were planted and until they grew together to form something called a hedge. Then neighbour wanted to do a land grab!
Why not have a chat with these people?
http://www.resolvemediation.com/index.php?option=com_content&task=view&id=43&Itemid=70 They may be able to give you some advice even though they don't cover your area. It should be free of charge.
P.S There this in High Wycombe
http://www.mediationbucks.org.uk/ and this in Farnham
http://www.mediationfirst.org/ Others can be found using this website
http://www.findcommunitymediation.co.uk/index.php