Advice on Tall shrubs or plants to screen out our next door neighbours

[Mercedes]

Next door's garden slopes above us and they've got their children a trampoline. It means they can see straight into our house and when we sit in the garden I feel like I'm on display and there's no privacy.
Although we have some fencing panels alomg the patio we need advice on what shrubs or plants we could use which are tall.
They would be facing south but would get some shade from a tree when sun passes behind it and top half of garden would get shade from a big shed from the west.
Any suggestions?

can you put some trellis along the top of the fence and grow a climber e.g. a honeysuckle? That way it won't be overbearing, grows pretty quickly and gives gorgeous flowers!

Get a small tree or a rhodendendron - they grow really tall and are evergreen.

bamboo is lovely but need to get a variety that doesn't have too rampant roots

We have a similar situation. We've just planted bamboo - phyllostacus nigra or aurea (nigra has black stalks, aurea usual colour) plants which are 5 foot high and within 10 days they're sprouting lots of new growth. This variety is good as it is clump forming and doesn't send out loads of roots. Rhizome forming varieties are the ones to avoid. The one we've bought also has foliage right to the ground, which some bamboos don't have ie they get quite stalky. It could grow as high as 15 ft but we'll keep it trimmed at around 6 feet. It's also a very robust plant and as long as it gets lots of water will grow anywhere. We also have trellis and are growing a couple of Solanum, which is a variety of jasmine. It's fast growing, flowers for around 10 months of the year and is evergreen. Don't buy the purple flowering one for trellis as it gets very woody, very quickly. The white one is manageable on trellis but you have to be quite ruthless and cut it back annually. They're in the plant shops around this time of year - by next month it's quite hard to find them. We had honeysuckle before but it too can get quite woody, however, if it's cut back regularly it is great and smells lovely.

The stuff about the bamboo is really helpful. For the trellis to really work the fence would have to be 6ft tall and then have trellis on top. The rear fence used to be 3 bars and folliwng the storms in winter it fell over and we're still waiting for our neighbours to put the fence back up. If we suddenly put up really high solid fence and trellis it might send out a very anti-social method to our neighbours. They're nice and altho the sightlines from the trampoline put us on show I wantto do it subtly. I'll look the bamboo and the other plants up.
Thanks

You can also plant the bamboo in pots or planters. We did this in our paved courtyard and within a year it had grown tall enough to block out the neighbors. There is lots of information about bamboo on the internet....do your research. Also if you are in the London area, go to the palm centre in richmond (or thereabouts) and see the bamboo in person.

We have bamboo too to screen out neighbours. No idea what variety though as the landlord arranged it for us.

The other nice thing about the bamboo is the lovely swishing noise when the wind blow it slightly.