How do I embrace my neighbours climber

Any clematis but Montana, I hope. It's wonderful in the right places but can be a bit of a thug if it invades where unwanted. It could, as you fear, also pull down a less than sturdy fence.
Leylandii, if controlled, can make a neat hedge but allowed to grow, they are just an unsightly menace.

They are not allowed to grow more than 2 metres on a boundary, are they?

not yet, I cannot get up high to see the leaves and it has not really crept under the wooden bit yet. Maybe the pwner is pulling it out from the gap between, who knows.

The first property I looked at was in the supposedly (changed my mind since) location. A beautiful wne well built new bungalow, built low, so I looked at planning objections before I viewed, I was first viewer. House on right had sent a strong objection in, enough for me to sit up and take notice. Went to view and stood on tiptoe, looking down the r side of the bungalow, just a metre wide space, with a rickety old fence, obviously the neighbours, then I saw them, horror or horrors, the line of closely planted leylandii tops, just peeping up and you would have to be a gardener to know what they were. Maybe 40 inches from the side of the bungalow. I viewed, loved the house but ran. The next viewer bought it and every so often I drive past slowly and can see these demon trees getting taller. three more years and the bungalow owner will have real problems

can you take a photo and post it?

yes it has aerial roots and is wandering into the gap below the wood standing on the wall. Not ivy fortunately, it looks strong, not russian vine either. Not spikey, ooh might be honeysuckle but I cannot see over the fence to the tall bits, I am too short, no flowers yet. It isn`t jasmine and the bit I saw through binoculars didn`t look glossy, unlikely to be virginia creeper. If it flowers, I will be back

When I saw your title I immediately thought....with a pair of shears!

Count yourself lucky We have one leylandii behind us, thank goodness it's not more!

Its not dodgy, only looking at my fence, the back of me is only gardens and fences in parallel, the houses are to the right and on a completely different road. Old layout and they are listed buildings, higgeldy piggeldy. There is no chance of even ever bumping into the owner, unless by chance in a class. The gardens are very long and most are a maze of old style allotment, roses etc. Actually a lovely view from 3 of my windows. Red sweeping roofs that bend up and down in the middle, little windows, tall chimneys. I digress, just need to work out what I can plant myself in my completely bare new garden.

It was Alimas post that has hit the spot, I was already thinking that at least it is not the dreaded laylandii. I will adapt

You can trim what is hanging over your fence; you're supposed to offer back the trimmings,ubut will they want them?
It would be best to ask if they mind you doing that though.
We have two montanas on archways and they were an absolute picture in May.

I don't think they have aerial roots though.

I would not mind a Clematis wandering over my side of the fence as they are easy to control, early varieties will have finished flowering and will die back in the winter. Now if it was mile-a-minute (Russian Vine) I would be worried.

It is possibly a vine with aerial roots. If so it will die back in winter

18" in a few weeks? Sounds like a triffid. Beware.

Or leylandii

It could be worse-----Japanese knotweed.

If you've only been there a short time, then this is the ideal opportunity to get to know your neighbour. You don't seem to know them or you wouldn't be using binoculars in their direction, always a dodgy thing to do.

Your garden is empty so you could use this as an excuse, if you need one, to ask what they'd recommend as easy-care plants.

Please don't get anxious about this, it's a solvable problem.

I know you won’t want to hear this but I think clematis are so beautiful I envy you I d love one flowing over my fence

Clematis Montana should be over or going over by now but provides a wonderful burst of colour in late Spring. I’d say enjoy it.

Who owns the fence?
Have a word with your neighbour and ask what the plant is?

Just keep telling yourself at least it isn’t a Leylandii.