Conifers have gone - What next?

I have just had four large conifers cut down at the rear of my garden. This has brought a lot more light and space into the garden but as you can see below there is now a privacy issue.
The space is south facing and there is a mature honeysuckle and jasmine against the fence, there is also ivy. My soil is neutral and fairly free draining.
The question is do I grow a new fairly thin hedge that can be kept to a sensible height.
Do I plant a specimen tree to give privacy in the summer, I was thinking of a silver birch one of the smaller varieties that grow to about 20 feet or so in ten years.
or is their another solution.
Hi from Kingswinford in the West Midlands
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I'm only suggesting this as I've just bought one, but how about dogwood for some hedging? You'll get lovely coloured stems throughout the winter and should be able to cut back easily enough if you want to.
Those are two very different pictures!
Betula utilis, planted where the obelisk is - to take the eye away from the fence?
Or, hoheria sexstylosa 'Stardust', nearer the fence, airy pale satiny-green (EVERGREEN)
Or, prunus cerasifera 'Nigra' for a striking purple summer presence (DECIDUOUS)
Or, one of the taller pittosporums such as 'Garnettii', which will fill half that space ultimately (EVERGREEN).
H-C
I'm not sure how much privacy a silver birch will give or how small it's realistic to keep them . They can be tricky to prune well, plus have the added problem of dropping twice in a year (catkins and leaves) as well as coating things in sticky sap.
Perhaps an evergreen Rhododendron would suit your corner? Or if you aren't bothered to maintain acidic soil or have flowers Griselinia is quite an attractive evergreen.
Ooh some interesting suggestions, keep them coming, I'm going to investigate them all.
The silver birch Jacquemontt will grow to about 30 ft eventually so a good choice I think. The white trunk is fabulous.
Hortum, Really like the idea of hoheria sexstylosa 'Stardust' but I'm worried it will not be hardy enough. Anyone grown one in the Midlands.
Hazel, I was just considering Pyracantha when I checked the thread, an orange one would be good. The blackbirds like them and I want to put something back for wildlife, the birds are not appreciating the loss of the trees at the moment.
Bob, Griselina looks good but is a bit too slow a grower I think.
Will check out the Dogwoods Dewdrop but don't you have to keep them small to get the colour.
Verdun, that combination sounds interesting, I'll check out the silver birch you recommend Hogweed.
Thanks for all your help.