Leylandii is now classified as a hedge and has to be kept to 2m. So you could give yourself more problems than it solves. I dont think you will find any tree that ticks all your boxes. A Mountain ash would defuse the light.

The problem with trees is that they will not just grow to the height required and stop. Birch, Ash, Italian Poplar and Rowan are all upright growers that fit your requirements, but all will be at least 10-15 metres tall. What you can do is prune them early, say every other year from year 3 and they will tolerate pruning better.

Juniper Skyrocket and Italian Cypress are evergreen trees that are tall and thin. Juniper Skyrocket is probably the best out of the bunch, looks good and will take pruning.

Fargesia Murielae is a good, thick bamboo. They like damp conditions, so you need to think of mixing thirsty trees with thirsty bamboo.

I have grown Viburnum x bodnantense 'Dawn' for just this purpose. It is not evergreen but has lovely pink flowers in winter. You can let the stems grow as tall as you wish and eventually prune some down to where you want most growth and also prune some stems to ground level.
I know this is not quite what you requested and may not work for you but it has for me. It has reached over the height of a garage roof.

We are very overlooked as we moved in. Our shrubs/trees that 'get up ' fast are buddleja, mahonia, ribes, a camellia already in situ. Viburnum semi evergreen. The biggies are Hazel, Hawthorn and a very rampant upright Laburnum. Our rowan is pretty old but kept in check by a choisya planted next to it and the hawthorn. Trees that keep leaves will shade out too much: just to stop neighbours looking at your garden activities ,if any? As deciduous trees mature their twigs blot out detail. Who goes out in a bikini in the winter. Or has a BBQ a distance from the house with shivering guests?Add a canopy over the patio near the house, as we did soon after we moved in.

A non-gardening answer. Do you know whether your neighbour had Planning permission to build the extension? A quick check with the Planning office will tell you. I can't imagine permision being given for an extension with a window overlooking your property. Also, there are Building Regulation rules that prohibit openings adjacent to a boundary because of fire danger.

I can Bernard, my neighbour built a utility room on the side of their detached house - they didnt need PP as it was less the a certain % age of the house. Its window looked across my patio and back door as they were raised up above us we were aghast but stuck with it.
When I asked the PP department they said they could do this and suggested asking them to put obscured glass in the window this they refused to do until they needed to use our land for drain access and then we were able to trade the glass for the access, it was ok till they opened the window.
And it seems with the new relaxed PP laws this situation is going to get worse.

Thank you all for these answers, left us with a bit of research to do!!
Thank you

:))