Eddy Bentley wrote:

Maybe there's something that somebody will say that could be of help in
the following situation.

snip

Have I got no legal rights in this situation?

I suppose this may vary from area to area, company to company, but I'm
in much the same situation as you in South West Wales. A similar
tree-murdering company came round two years ago and wanted to cut back
an oak growing beside-and-under an 11,000 volt line, for which a 3 metre
clearance is maintained. That would have meant felling the tree, pretty
much. The tree is right on the property border, but just on my
neighbour's side, so I referred them there. My neighbour refused them
permission and, after some attempt at persuasion, the contractor said:
"we'll just have to put it down as a non-comply" and left without
cutting.

That phrase suggested to me that neither the power company nor the
contractor have an absolute right to do as they wish and would have to
get a court order if they were determined to have a tree cut back
against its owner's wish, and that may be too much trouble for them.
More likely, I suspect, they would leave it until said tree fell over
onto the line, or caused a serious short to earth, and then the
non-complying owner would be sued for all the costs of repair.

HUGE CAVEAT: this is just my surmise based on this experience, I'm not a
lawyer. If you really want to keep your hedge as is, you might want to
consult a solicitor who's knowledgeable in this area.

They ask "permission" to cut, but the tree-cutter has warned that if I
do not agree then he has the ability to inform the power company and the
power company has the right to turn off the electricity supply!

Purely an attempt at intimidation, I suspect.

Brian Mitchell