Everyone has their own favourites when it comes to hedging. I would say that evergreen, broadleaf and mixed has its place in a rural setting. I think that you will find that a mixture will have hedging that will grow at different rates and will require a greater management than perhaps a single species. For that reason, I would suggest that Taxus, (yew) would be my choice. I will not be too rampant and has few enemies and will look neat and tidy and easily managed.

Thanks for our suggestion, Jimmy, but as the neighbour won't do any trimming on his side, we'll end up with the same problem as we currently have with the privet hedge.

This is a bit of a conundrum - fact is, nothing will look good if its only maintained at the top and one side, and an informal mix of hedging will look messy without any training or pruning.

It occurs to me though to wonder whether, if you remove the privet (if you're allowed to, maybe its half your neighbour's anyway, whether he maintains it or not) can you not then plant within your own boundary, a bit further in, so that you can access both sides of the hedge whilst still standing on your own land rather than on the neighbour's side?

the only other thing I can think of is to plant something like Berberis darwinii in a row, a bit closer together than you would with a single plant, but not exactly as close as a maintained hedge would be, and let them do their own thing, growing together at will. Or, if you're allowed, take out the privet and install a fence instead.

How about Lonicera nitida? You can get away with trimming it annually and it makes a very neat hedge when closely trimmed. Like nearly anything else it will get fatter on the neighbours side unless they allow you annual access to cut it but keeping it neat on your side and on top should be pretty easy. There is a green one and a gold variegated one.

I guess the problem is the neighbour. have you thought about offering to trim the hedge for him/her? they may not have the machinery or knowledge about how to do the hedge. Either way if you replant then in time you will be left with the same problem.
we trim both sides of one of our hedges. at first we thought it was because the neighbour was 'interesting'.
however one day the neighbour on their other side said they had told them they were scared to tackle it in case they killed it and upset us. [ I can understand them not upsetting my OH he looks like a Berserker Viking]. They are still 'interesting' but the hedge is now how we want it on our side.

I would try diplomacy as Seaburngril suggested. Simply walk over there VERY NICELY and ask VERY POLITELY if you can come over to trim the hedge. How could he refuse? Would the sky fall if you did that? You're going to have deal with him on some level regardless of what you do. Can you unilaterally decide on your own to replace/remove a property marker? He should be consulted before you change anything.

hi,
Ive seen cypress goldcrest grown in a tight row which are quite good as an easy to maintain hedge and look good. I had one in my old garden which grew to over 5ft so would just be a case of taking the top out to keep to desired height, plus they have a lovely lemony scent. Good Luck!

Thanks for all the great replies. Some interesting planting suggestions we hadn't considered, so I'm feeling a bit more optimistic now. :)

Discussing anything at all with the neighbour is sadly not an option, for reasons I won't go into here. The hedge in question is our boundary hedge, so we can remove it without getting his permission, and without encroaching on his property, thank goodness.

Thanks again, folks. I'll let you know how it goes. :)