I'd dig a trough 18 inches to 2 feet deep and a foot to 18 inches wide along the fence, line it with root rhizome barrier and plant Phyllostachys (a variety of bamboo) inside it. There's one with yellow canes and one with black ones... gets about 13 feet high, perfect height. You may read that you don't need a root rhizome barrier for this particular bamboo, but in my experience, you do... they're not cheap to buy, but they do spread quite quickly, so buying, say, 3 means it'll be all along there in 3 years.

Did they get planning permission to do this ?
Might be worth asking. Blocking a neighbour's light
is not allowed.

Sorry Diane there is no right to light!

Yeah, but the neighbours sound as though they will complain about exactly that issue as soon as anything obscures those upper windows of the conservatory...
My first thought was to set up a trellis fence-topper, say 6x2', but attached to battens on the wall rather than onto the fence direct. That way you could plant some Russian Vine (for speed) which should give a little cover this summer, and after it's got its roots going it'll cover their windows every summer no problem. Of course it's rampant so you'll need to be savage every winter with pruning, and it'll give no winter benefit, but it's fast and cheap.
Then I thought go with the bamboo, root barrier on your side, to direct all the concrete-penetrating roots into next door's foundations... best not, though...

Not strictly true Mg.

"A "right to light" is an easement that gives landowners the right to receive light through defined apertures in buildings on their land. The owners of land that is burdened by the right cannot substantially interfere with it - for example by erecting a building in a way that blocks the light - without the consent of the benefiting owner."

The Law commission have a consultation paper regarding this which makes interesting reading.

Might be the case in England but not in Scotland… at least so far as I am aware and enough folk I know have tried to stop extensions etc. that will block their light without success.

I think it is the case in England as there has been a lot of
trouble with C Leylandii hedges growing too tall & blocking out light & people have been forced to cut them down. I believe there is a law in place concerning this light problem now.
( the Russian bindweed would probably come up through the floor of their conservatory)! That would sour relations somewhat.

thanks everyone, interesting ideas. Like the sound of the bamboo idea so will try and go with that idea. I think they didn't need planning permission because the planning laws were relaxed. Know they had something there when we moved in, it was just that we went out one day and then came back and it was knocked down and this new conservatory was there half built, that was even bigger, longer and higher up. If that had been there when we bought the house, I probably wouldn't of bought this house. The builders even had the cheek to ask to come in the garden, take the fence down to finish the conservatory. My husband stupidly let them in. Couldn't let the dogs in the garden all day. Didn't get any thank you's. Even if the kids ball goes over there fence they pop it! such a shame as all the other neighbours are lovely. Will just be nice to not feel like we are so overlooked by them.

Scottish Law is quite different to English law M.G.
This applies particularly to Public Rights of Way.
I walked all the way up the south side of Glencoe
quite freely.
Couldnt have done that in England.

Indeed in Scotland we have the 'right to roam'.