How to make a garden more private?

[Pannacotta]

We have recently moved and the new garden is a good size but is quite overlooked on two sides, theres a two storey block of flats close to one of the boundaries.
Theres a very tall "hedge" of leylandii by the flats, but am having it cut down as it shades most of the garden, any ideas on what to replace it with?
The two borders face North and East so not too sunny. Would prefer native trees/shrubs which are mainly evergreen good for birds/wildlife, if thats possible....
Any ideas on what we could plant?

Bamboo?
We are putting in tall photinia, (red robins) they are evergreen but not native.

Birch would be tall enough, native, and provide dappled shade, but not evergreen.

We have bamboo and it grows fast and can be very tall.
Most of our privacy comes from the silver birch in the middle of the garden but they obviously take a good few years to get really big.
Next door has bay trees and they seem to grow quite big quite fast.

Got room for a beech hedge? Will take a while to grow but you can't beat for wildlife-friendliness. Brill for bird nests.

Hawthorn good and can come in standard 'tree' variety too

Will have a look at all the above, whatever we choose needs to be very tall, was pondering leaving a few leylandii and planting other things - such as birch/beech in front to break up the expanse.
Am thinking of using bamboo in another part of the garden where the exotic look would work better.
Thanks for all the suggestions.

holly is nice - dark and evergreen and lots of different ones. with some hawthorn mixed in? not evergreen but thick and bushy

Leylandii are horrible.

Could you grow a beech hedge? They are so thick when properly grown.

I clicked on here hoping to get ideas but became depressed by how little I know garden-wise vs how I would like my garden to look!

Does beech grow quite tall? I do like beech hedging but think as an alternative to the trees it might be a bit short?

Beech can grow as tall as you want - we've had pretty tall border beech hedges in various gardens in our family. You'll probably need a specialist beech hedge cutter to come and cut it for you once a year as that is very hard work.

Beech goes through a wonderful spectrum of colours through the seasons, from palest green in spring to deep gold in autumn.

If you haven't got room for a hedge what about a fence with quite high trellis on top and then you could get a fairly vigourous rambling rose or clematis to grow on it. There are some lovely shade tolerant clematis and roses and they would be green all year.

Or you could build a wall? And have creepers growing over it.

My parents replaced their front hedge with a wall four years ago and it already looks as if it has been there forever (the house is mid 19th century). They did quite a bit of research into architectural style, quality of bricks etc before building to ensure they got the right look, and when it had just been built my mother and I painted it with yoghourt to encourage the lichen . My parents then planted clambering roses, a wistaria, a honeysuckle etc and it now look fantastic - and lets much more light into the house/garden than the old hedge ever did.

For the possible height of beech hedges look here.

Thanks, will have a think.
Thats a VERY tall beech hedge Purplefrog