I have a patch of garden in permanent deep shade. Ferns grow well there, as does ivy, cotoneaster, and even a peony. Primroses do ok, also calendula (granny's bonnet). Careful if you grow calendula, because if you do you'll never get rid of them.
Yes, I'm on clay, thick boggy clay (Croydon), and yes they do well.
A good tip, if you are not sure what to grow, wander around and see what is doing well in neighbouring gardens, either by accident or design.
I've actually got a pair of rhododendrons doing well in shade in a clay garden, but I did dig in about 300 litres of ericaceous compost. It was a little experiment, and it has worked.