Phone your local council building control department. They will be able to tell you the legal position and be in a situation to ask your neighbour to cut the height to the legal limit (of 2m I think). Why have they built it so high. Is there a privacy issue for them of your being able to look in to their home/garden? If they have the space I believe they could grow trees which might be even higher and depending on where you are in UK that will not be covered by the high hedges legislation in England. Sorry cannot offer more advice.

If your conservatory is right up to the boundary line they may well feel it is an intrusion in their lives. Did you talk to them before building?

6ft with out planning permission, he's being naughty!!

I had hellish time with neighbours involving conservatories being built 3 feet about ground level to start with. Meant I would have needed at 9ft fence at least get privacy. I fought tooth and nail with the planning ... it got thrown out at local level due to privacy issues but they went to Scottish Exec and I didn't stand a chance. But they did have to put in obscure glass on my side :) it didn't stop him standing at his door and staring in my windows though!!
Is your floor as high off ground level as my problems were or are you at ground level??
I can sympathise with your neighbours having been in their position but now I'm a conservatory owner, but we're not overlooking anyone :)