There was a thread on this forum some weeks ago that would give you some names of plants to try. Maybe you could google your way through that thread, looking to see which are most adaptable to chalk - assume from this your soil is not acidic?

I don't think you'll get much in the way of flowers, scents, and other typical "garden" look, but you can get greenery, weed suppression, erosion control, and some flowers!

Here is a link that might be useful: Evaluating shade groundcovers

I have just read the previously recommended thread. Plants vary in different climates. In our woodland it is the shallow rooted drought tolerant plants that have been enduring. When we moved here in 1986 the wooded area of our property had become a jungle. We cleared paths and vines and left most of it untouched. We had some beautiful 'surprises' of already well established plants. These are seasonal, mostly blooming in spring. The predominant ground cover plants are wood anemones, wild phlox, periwinkle, and spiderwort. Ground ivy is also a predominant ground cover but can become very invasive. However, it is not unattractive and the early blossoms provide nectar for insects. Spiderwort is growing directly out of cracks in red granite rock. We have relocated a few things into the wooded area along the paths. Lycoris (both squamigera and radiata) have done very well. It has a short bloom period but the plants in the shaded areas come up and bloom sooner than the plants in the open garden areas. A day lily that will grow and bloom in the wooded areas is the common orange day lily AKA 'ditch lily' that is very common in our area. We have introduced some plants into our shaded door yard and garden areas such as Solomon's seal, blood root, wild ginger, meretensia, and small bulbs such as crocus and star of Bethlehem. Iris has thrived in semi shade and day lilies have done well beneath trees. Dame's rocket (hesperis matronalis) grows as a wild flower below the trees and will spread if not controlled. EP

I notice you state that you can't dig holes in rocks. Most of our gardens are growing or have been built over sub surface of solid rock or chunky rocks. I have had success by putting divisions of day lilies or iris on top of a clean area of ground and filling around the root divisions with soil. Also, I will take the seed stalks of plants such as cone flower or salvia and lay them in piles where I wish to start more. The seeds drop onto the earth and germinate. Have expanded our gardens in this manner. We have also thinned out the trees in the area around the residence to promote more light. Good luck. EP

Plant seeds...no digging required! That's what I do around the roots of my old maple in the back yard.