Lots of Primulas would love that sort of situation. P. japonica, especially and they come in lots of colours from yellow through to red.
Obviously almost all Ferns thrive in damp shade.
Tricyrtis if the soil is full of humus.
If the soil is acidic you could try the Meconopsis.
I could list dozens more.

Thank you Owdboggy will have a look at your suggestions.

I envy you, damp shade. We have plenty of shade here, but it is very definitely dry.

Podophylum [spotty dotty] also does well, some hostas tolerate quite deep shade. heucherella, tiarella, Telima, Mitella, some of the ranunculus too. larger plants include ligularia too.

Thank you Seabournegirl will look at your suggestions.

Astilbe are good if it remains permanently damp, but in my experience, damp shade turns out to be dry shade during the summer months...Pulmonaria will do well too. Otherwise, for shrubs, Prunus laurocerasus 'Otto Luyken' (dwarf cherry laurel) should do well, and for a slightly larger shrub, Mahonia aquifolium. If your soil is not alkaline but neutral to acidic, Skimmias should do well too - S. reevesiana is an hermaphrodite, so will produce flowers and berries, but it does have a looser growth habit than many other Skimmias.