Can Neighbour do this without permission?

leighclancy

if it doesnt cross into your properties "floorspace" so to speak, then youll have a tough time getting it removed. unless its blocking some kind of view? as someone has said they may need planning permission, so go to the council and check of they have. if not they will have to remove it

leigh.

macman

You say it is a 'shared' fence, but it must belong to one or other of the houses. If it's yours, he is not allowed to attach anything to it without your permission, not even a trellis. He can build an inch from it, but not attach directly to it.
Maximum fence heights vary from authority to authority, but 2 metres is the norm. So if he has effectively raised the fence above that height he is probably in breach of the regs. It's difficult to understand how this has been constructed from your description, so posting a picture will help a lot.
Your next step would be to visit your local planning dept armed with a few pictures so they can give you some info based on that.