Thank you all for your helpful input. Your responses and advice are a
lot more bountiful that I was expecting - especially so soon after
posting! (I am new to newsgroups).

In answer to Kay's question, there are actually 5 trees within a
narrow strip (approximately 15ft x 2ft). Firstly a mature walnut tree
which is thriving. Adjacent to them are the three elder trees, and
finally the cherry tree. Unfortunately, I'm not experienced, and have
not lived at our home long enough, to tell how old these trees are,
but it looks like the elder trees are much younger than the cherry and
the walnut. When I first moved in a few years ago, I can't say I
remember the elder, but I certainly do remember the walnut and the
cherry. Now that my neighbour has pointed out the issue, I do realise
that the cherry is bearing significantly less fruit than when I first
moved in. Is it also possible that the walnut tree is having a
detrimental affect on the cherry? In terms of size and stature, the
walnut and cherry certainly overshadow the elder.

I think that the preference to remove the elder rather than the cherry
is probably due to the precendence it takes in maturity and
establishment. My neighbour has lived at our location much longer
than me, and is probably more attached to the cherry, so the request
to remove the elder is not necessarily based on which type of tree is
more likeable. We do get on well with our neighbours, and I am happy
to comply.

Could anyone advise me about how I find out whether there is a
preservation order? I only remember a mention of the fact that I am
in part or possibly wholly responsible for the maintenance of this
strip of land during the conveyancing process before I moved in. I
should have done my homework better! Perhaps I could just dig up some
photos taken after we moved in to try to see if the elder were so
established.

If the elder is able to rejuvenate so well, even if I cut down to the
stumps, then does this mean that if I do remove the main trunks
without further using a killer, and the elder was not actually
responsible for the cherry's demise, then we would still be in a
position where the elder would grow back, and the damage would not be
irrevocable?

Thank you all again,

Mark