A photograph of the area would be really helpful, if that's possible, but some questions - how steep is the slope and is it mostly in sun or in shade? And when you say mediterranean climate,does that mean this area is not actually in the UK?

Intriguing. It would be useful to know what the soil is like, too. First thoughts are Rhodohypoxin, Gaultheria and Cornus Canadensis.

Is the area actually shaded by the tree? Is it a mature tree with widespread roots?

Hmm...Sheilabub, I think that Cornus canadensis wouldn't like a Mediterranean climate much. My choices would include Thymes, ornamental Oreganos, and low lying Germanders in the sun, or maybe Vinca minor or Mahonia repens in the shade. In the sun, a few well placed bulbs of Saffron, winter-flowering Crocus, Freesia, Poppy-Flowered Anemone, and/or Tulipa saxatilis would provide color when the groundcovers weren't blooming.