Shrub suggestions for a mainly shady alkaline bed.

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.

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.

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.

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.