Tree Selection Advice

A tall variety of Cotoneaster would definitely work ... and the bees adore the little flowers, while the birds love the autumn berries. Easy to prune, easy going, cope with drought, evergreen (well, almost - can look a bit bare by Feb before the replacement leaves break through). Perfect.

 

Not as perfect as something from here...Artificial Trees - The Artificial Plants Shop No maintenance, no root or leaf problems!

 

Oh my goodness that's such a sad sight...really expensive plastic

 

They aint cheap, are they.

 

You can say that again! Madness!

 

Not so bad compared to French GC prices As with everything else, you pay for the convenience. Save on compost, fertiliser, water and possible replacement too!

 

Not really any sadder than seeing a living plant being constrained to a totally unnatural and quite possibly abridged life!

 

If it's a totally enclosed container, as opposed to one that's open to the ground, it's certainly a bit small for most large shrubs/trees, so bigger will always be better for the health of any plant you choose. The mix it's in will have to be suitable too - a good soil based one, or just soil, but with adequate drainage. Anything in a container needs far more attention than in the ground, and they all drop foliage at some point, regardless of what they are.
You could try good ol' privet. It can be grown successfully in containers, and either treated in the usual way as a hedge, and be trimmed, or it can be left to grow. It will become a tree if left to it's own devices. The yellow/variegated one is nicer than the plain green. If you're in a colder area, it'll be semi evergreen though. It's not strictly e'green, which many people tend to forget.
Portuguese laurel would be ok, as long as it doesn't dry out, although it can recover well enough in the ground. Fatsias would be good, as suggested, and will grow in containers, and can be pruned if needed.

Those flamingo willows[ if that's what you mean] aren't evergreen, and they'd need loads of water to keep them happy. They're grafted, so if the main plant dies for any reason, you'd end up with ordinary willow. That could be a problem [or a blessing depending on your view of the flamingo ones ] but it wouldn't be a great choice for what you want IMO.
Bay trees can be ok if you're in a suitable part of the country for them, and this is why it's important to know your rough location for suitable advice to be given. When you say the fence is SW to NE facing, which side is which - ie which side is the planting facing?