I'd go for green - a Fatsia Japonica maybe?

I agree with the Fatsia suggested by Wagger, but have reservations about planting there - it appears to be pretty close to that large tree growing through the fence, and thus the soil will be impoverished, dry and full of roots. How about just fixing a trellis section between the shed and the fence and the front of the shed to disguise the gap. I also note the shrub on the right against the fence - is that something which will get large? If so, it will exclude light from whatever else you plant further back.

The shrub on the right is an Azalea. It was given to us by a friend last September, which was when I put it in the ground. It has neither grown/flowered nor died so I'm not sure how it's going to end up. Yes, the tree growing through the fence belongs to our neighbour.

I've just googled the Fatsia and it does look lovely. Another option might be to get one of those narrow trellis with a planter at the bottom but then I'm not sure what to put in it.

At least the plant(s) at the bottom of the trellis would get more light than if they were stuffed into that gap behind the shed.

I think a Fatsia would get too wide to be comfortable in the gap between the shed and the fence and I think it'll be too dry & dark to get anything at all to flower.

You could get one of those garden storage bin things and put the overflow from the shed into it.

Hmm, well when I agreed to the suggestion of a Fatsia, I was thinking it would be planted slightly forward of the shed, so that as it grows it disguises the gap behind, but isn't actually in the gap, if you get my drift.
Those trellis attached to trough things you're talking about are a waste of money Sgbabe - nothing that climbs will tolerate having such shallow root room, so the only thing you can plant in them is low growing stuff.

Fatsia Japonica can get thin and leggy when in semi-shade - the shade stunting growth whilst the afternoon sun makes it grow. If you want thick growth from it then it needs either full sun or shade. I suggest a clumping Bamboo as it will like the growing conditions, give an evergreen colour, will grow quickly, provide cover and makes a lovely soothing sound when the breeze caches it.

Fargesia murielae is very hardy and is not invasive.

where is your compost..perhaps that could go there..or mushrooms?

I haven't got a compost heap, I get ours from B&Q! I've put a small picket fence there for now but still thinking about what to put behind it. Compost box might be an idea. I like those bee hive ones.

WHY DON,T YOU PUT SOMETHING PORTABLE THERE ,A PLANTED TUB ,SO YOU CAN MOVE IT IF IT DOES NOT FLOURISH, OR HOW ABOUT A STATUE OR SOME SORT OF INTERESTING OBELISK .IT WOULD ALSO BE A GREAT PLACE TO STAND A WHEELBARROW /

Dear friend,
While it may be of no interest whatsoever, I wonder if I might suggest, rather than specifically making a barrier, which may well look "obvious" as being so intended, you might consider painting the shed a drab green or "woodsy" brown, and positioning a wide-squared trellis - (I note a prior comment, however ...

... If you have "shallow" ground, there is nothing at all to stop you from bringing in soil and building your own planting bed or berm) - on the diagonal ... A trellis of any description which appeals to you, painted in a "garden hue" and positioned diagonally, will not only "naturally" lead the eye past the shed, but will give you greater options for planting a garden bed with a variety of shrubs, even climbers, which will give a delicate appearance as opposed to an obvious attempt to obstruct.

This could be turned into a beautiful corner indeed!

Simply because your ground is flat, shallow, or otherwise, does not mean that you are obliged, or restricted, to leaving it that way.
It is only a suggestion made with the best of intent.
Yours sincerely,
Philip Livingstone

Thanks Philip for the suggestions. We've put up a little white picket fence and planted a little 'woodland' area where the rhododendren is now. We added a Mahonia Charity and a shrub so that should 'hide' the area in a few years' time. :-)

Thewoodlan idea sounds okay and you don't need too spend a fortune. Depending if you have small children or not. You could always have a small water feature and a wild garden with nettles but always remember what takes a few hours to do when you are young maybe impossible either when taken ill or get older or by yourself. If you are out walking and you see someone pruning a nice shrub you fancy ask if they mind if you can take a bit with you. People say there are special times of the year to take cuttings but my belief is if the cutting is free then any time of the year is okay. Has two chances. Just wondered if you liked wild life and you planted a Buddleia. Not a very tidy plant but back fence is similar to your side fence near the shed.
I have a large tree growing close to the other side of my fence and as BAMBOO mentioned the soil is impoverished, dry and full of roots. However my Buddleia grows very well. I do water and feed to compensate the 34 year old sycamore. However you must keep it in check. Not only does the shrub give me privacy from the 3 storey block of flats built near to my back garden but makes an excellent feeding station for the many birds that visit my tiny back garden. I do not prune all the branches so this has left some branches strong enough to hold nut and fat feeders for the birds and squirrel. Also adds protection from attack by predators from above. Helps the UK butterfly and bee population have a sip of nectar. The shed windows would make good viewing to take some wonderful nature photos.
Other members might know a lot more than me but I checked on the tree on the other side of my fence and was looking at the Triffid that is moving in on your garden: Trees growing in a garden belong to the owner of the garden, but if the tree straddles the boundary and extends its trunk and roots over the boundary, it is owned in common by the two landowners. Check out in case the tree ever does come down but don't fall out with next door.
Noticed the shed has nice curtains, would make a nice dog house for me or to keep a few Singapore tiger beers .
Good luck to you and hubby with the garden Sgbabe
Regards
Tom