Shade tolerant flowering annuals grown on from strong young bedding plants (growing from seed is not easy in shade) do well in light to medium shade but do not bloom well in heavy shade. Some annuals in fact prefer light shade to full sun. Impatiens come in a wide range of intense colors and heights. Browallias, Coleus, Wax begonias and Dwarf salvias all tolerate light shade.
If you like growing from seed, flowering annuals can be started indoors or in a greenhouse and then when big and srurdy enough, transplanted into the ground or containers. Some Spring flowering bulbs survive deep shade and providing, the leaves receive full sunlight for most of the day and are left to die back naturally to build up food reserves for the next blooming cycle, will establish and come up year after year.
Bulbs like Crocus, Scillas, Snowdrops, and species tulips bloom and produce leaves before the trees are fully in leaf, so that they receive the light they need to blossom annually. Daffodils and English bluebells are natural to our hedgrows and open wooded areas.