many of the anenome japonica do well in clay. they can be invasive though in looser soils.

Hellebores thrive in clay as do primulas. I've got vinca minor established in heavy soil and some of the geraniums (G.sylvaticum, G.nodosum, G.phaeum and G.macrorhizum) will take shade

If you want larger plants, Mahonia aquifolium will do well (about 3 feet high eventually) as will Cornus alba 'Elegantissima' (though this, if left unpruned, gets more than 10 feet, but has lovely new red stems, so lots of people prune it right down in Spring to encourage bright red stems which you then can see in the winter when the leaves drop). Good groundcover in such a situation from Lamiums - have a look at L. White Nancy

An awful lot of ferns are happy in deep shade and look quite beautiful. I love the way that dryopteris unfolds. Aquilegias cope happily in quite a lot of shade as do pulmonarias and bergenias. I find it quite difficult to know what we mean by shade - for example an area by a North Wall is often in deep shade throughout the winter but has quite a bit of light in summer. I found that English Valerian is beautiful there. On the other hand deciduous woodland has a reasonable amount of light in the winter and much less in the summer. Here you can put any number of early flowering spring flowers such as anemones and bluebells that will have died down naturally by the time the trees leaves come out.