Am I in the wrong ?

You say you have had to cut down your rambling roses, not that you have uprooted them. In my experience rambling roses will regrow so if you can erect some kind of support for them slightly in from next-door's fence, would that not mean you don't lose the roses altogether?

Why is a ten inch gap underneath a laurel a problem?

You cannot grow anything against the fence, but you can plant something in front of it that will grow to hide the gap.

I agree with the trellis idea. Friends of ours have done that and it works really well.

Yes, please put a trellis up a few inches inside the boundary. It works well.

Great minds think alike MissA. Have a look on Pinterest Beau1958, if you type ‘freestanding trellis’ into the search bar lots of ideas come up.

How about a freestanding trellis with ground anchors, and use that to cover the gap, for your roses to grow up without touching the fence?

Best to resolve it peacefully.
You could put up a trellis type panel on your side, so it blocks out the view of the fence, but doesnt touch it.

Then you could have an absolute riot of plants growing.

Yes sorry it’s 10 inches. All the ivy and roses were there when we moved in. He’s told me not to grow anything up against it so I’ll just have to look at a boring fence now.

It's a shame your neighbour couldn't have handled the situation better Beau and I can understand why you're so angry about it.

How big is the gap? 10 inches? centimetres? you don't specify in your post.
As Avalon says, its his fence, and strictly speaking you shouldn't be using it to support your plants to technically you are in the wrong.
Darned annoying all the same. Can you plant a flowering shrub in front of the gap?

That's such a shame Beau. Could you put up a fence on your side or is that too expensive?
My DB had almost the same problem with his neighbour and a mutual fence which like yours was the responsibility of the neighbours.

In the end my DB got quotes for a new fence, showed these to the new neighbours who agreed to go ahead and share the costs.

His neighbours were not gardeners at all and had no idea how important it was to DB.
It's all done now and flowers are growing up the new fence.

If it’s his fence then arguably you should not have been growing rambling roses up it. Maybe he thinks this has contributed to the demise of the fence? If he is replacing the fence it will be easier with nothing growing up it.

It is his fence so he can do what he like with it, not very neighbourly though.