Shrub suggestions for a mainly shady alkaline bed.

Mahonias would do well in dry shade and have lovely yellow sweet smelling flowers Inthink a good variety is Aquafolium ( I may not have got that exactly right). Also fatsiascwill do well in that position. Not the solder one, it is not as robust as the more common one.

I have a Fatsia in a pot near the hostas and it seems to like it there so that will be the first one in! I shall look up the mahonia.

I also have a Mahonia, which I’ve had at the end of the shadier part of the garden for many years, and it produces beautiful scented yellow flowers in the Winter, which attracts the bees.
My Cornus ‘Midwinter Fire’ also does extremely well in a shadier position, and has done for many years. It is striking in the Winter.

Skimmias will tolerate shade and most soils, I don't water mine once they're established so I think they'd cope with being under a damson tree unless we have a very dry summer.

Yes my skimmia only gets a bit of sun and has thrived. It needed watering the first year and since then has be fine and like the flowers. My golden leaved and small Acer seems to like it's shady corner and I planted it in normal soil. Viburnum, camellias and daphne seem to be fine as long as there is ericaceous soil put in the hole and a top dressing of it each year. The Daphnes smell gorgeous. As others have said Mahonias have ,lovely sprays of flowers and flower when there is little else flowering.

I would disagree about Daphne RedRobin but the others would work.
I have found Daphne very particular. She likes a sunny, sheltered corner with well drained soil. don't we all 😂
Weigelia and Deutzia do well in semi shade.
Skimmia, rhododendron, black elder, flowering currant and several I can't remember the name of. 😂😂😂

Depends on your soil -

I agreexwith the suggested shrubs and would like to add Camelia .
Mine were planted about 40 years ago and contribute a great deal to the garden without any effort.
Some are in full sun ,some dappled shade and some in full shade.
I once had to sponge off a sticky black mould on one - that's the only time I've had to do anything.
Otherwise , I just prune them after flowering.
If they have a tonic it's would be old tea bags .

Just reread your title and wonder ìf your alkaline soil might need some encouragement if you grow Camellias .
Mine is acid .

I suggest ;
Viburnum
Garryia
Berberis

Wow! A lot of choices. I shall draw up a list for our next visit to the nursery.

Here's some more ;

Hydrangea -as your soil is alkaline they will be pink unless you alter the pH .

Choisya -Mexican orange blossom though it might need a tonic to maintain green leaves.

One of my all time favourites - Quince /Japonica.
It's so useful if you want to keep marauding foxes /cats away from an area .It's very easy to grow and can be red ,orange,pink like apple blossom and pure white.
It produces a fruit which takes hours to cook ,but makes a nice jelly.

Enjoy your replanting .

I noticed plants listed which are not suitable for alkaline soil.
Any you like double check.