Daphne mezereum is tolerant of alkaline soil, but needs good drainage, so you might need to put it in a raised bed. It's deciduous and flowers on bare stems before the leaves emerge.
I think there's a daphne which is ok in clay, but it needs acid soil, like most of them. (I've just looked it up - it's Daphne pontica - greenish flowers.)
It would certainly be possible to grow D.mezereum if you can give it good drainage.
Since 2019 I've lived in east Clare, in the west of Ireland.
Clay isn't necessarily acidic though. There are lots of daphnes growing round here and our soil is heavy clay but mostly neutral. to acidic, so you might be better checking the pH and then deciding
It's a place where beautiful isn't enough of a word....
I live in west central Scotland - not where that photo is...
My soil is Essex clay that is very slightly acidic. A few years ago I planted a Daphne Tangutica. It is supposed to grow eventually to approx 1m. 5 years on mine is now approx 2m wide and 1m tall. I have given it some fairly harsh pruning (I know it's not a good idea with Daphne, but it's now completely covering 2 paths) so far it hasn't sulked or died. It is a beautiful shrub, but it's outgrown its space too fast.
We are on clay soil and had a fabulous Daphne odora for many decades. Last year it was very unhappy and growth was less and less. It gave us many years of great fragrant flowers.
We have replaced it with Daphne bholua Jacqueline Postill. We bought it last year and it has doubled in height and is covered in flowers (albeit they are smaller than odora).
Still growing in clay soil.
It was shown in one of the GWs programmes but can't remember which one.
I also have several daphnes growing in slightly acid clay with lots of organic matter added. I can highly recommend 'Perfume Princess' (in flower now) which is a recent cultivar and is much less fussy than my D. aureomarginata, which is just showing some colour in the buds, but will produce a stronger fragrance. I actually rate Perfume Princess as a general 'good doer' of a shrub.
A trowel in the hand is worth a thousand lost under a bush.
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I think there's a daphne which is ok in clay, but it needs acid soil, like most of them. (I've just looked it up - it's Daphne pontica - greenish flowers.)
It would certainly be possible to grow D.mezereum if you can give it good drainage.
I live in west central Scotland - not where that photo is...
A few years ago I planted a Daphne Tangutica.
It is supposed to grow eventually to approx 1m.
5 years on mine is now approx 2m wide and 1m tall.
I have given it some fairly harsh pruning (I know it's not a good idea with Daphne, but it's now completely covering 2 paths) so far it hasn't sulked or died.
It is a beautiful shrub, but it's outgrown its space too fast.
If you're not sure of the pH, you can get an idea here by clicking on search and entering your postcode
http://www.landis.org.uk/soilscapes/
Billericay - Essex
Knowledge is knowing that a tomato is a fruit.
Wisdom is not putting it in a fruit salad.