I'd go for an evergreen clematis, was going to suggest a rose but then you'd probably have to move the the tripod forward for one of those, also it would be bare during the winter months..

or what about a fastigate evergreen: the yew Taxus baccata fastiagta or one of the junipers like sky rocket. They would fit the bill and not need much maintenance.

I should have said that the obelisk isn’t staying. It’s only there as a marker for where we think the tree/shrub might go.
Thanks for the comments though. OH really wants a columnar evergreen but I don’t like them. So far neither of us is giving way!

I think a mountain ash would look lovely there. It's a beautiful tree and it's native. Birds love the berries too. Every garden needs a tree, I think.

i have a native rowan and i love it. but in the winter it wont 'hide' the shed much

Thanks for the ‘support’ regarding a rowan. One of the reasons I want one is for the birds as so many people here have feeders they’re spoilt for choice and, therefore, don’t use mine. I agree, though, that it won’t hide the shed in winter. But do I mind, that’s the question?
I’ll let you all know what decision we come to.

I wonder also if a different colour paint would make it fade into the background.

Although it’s a nice colour I didn’t choose the paint. I would have preferred a dark green or even brown. But I know that OH definitely won’t be prepared to repaint it! Sadly.
So far, I’ve conceded the tree as he’s adamant there are too many trees around us already which block out sunshine. I’ve made a short list of other possibles: Hebe, Edgeworthia (vine weevils ate my last one), Pieris, Fothergilla (new to me). Also Euphorbia Wulfenii. Not sure about the last though as I don’t think it’s tall enough.
Your comments would be appreciated.

If you want a taller shrub then Photinia Red Robin comes to mind its evergreen and the new leaves are a lovely red this time of year it can be left to grow or pruned to keep a certain size, other shrubs such as forsythia and weigela would shield the shed and can be pruned as needed. Dont forget that GOYpeadia has lots of photos of member shrubs in several categories for you to look at for some ideas.

If you are thinking about the birds how about a dwarf crab apple?

I think the solution would be to put in a big sweeping, curving path from the bottom middle of the first picture in a wide curve to your pergola. Then to the right of the path where the obelisk is plant an Amelanchier. A shrub-cum-tree it had white blossom in April with pretty bronze leaves.