Ground Cover in London

I am looking for a perennial ground cover plant, to grow in fairly dry conditions in partial or full shade. Something low and slow growing. What suggestions do you have please? The location is London England, which is actually quite dry contrary to popular belief about wet and soggy England!!

You do not say whether you want to stay with herbs or whether you are looking for any plant, from among both herbs and non-herbs. I will assume that you are looking for herbs mainly.
Because most of the common herbs require full sun the vast majority of herbs are not suitable for your situation. However, three herbs that come to mind are:
Sweet woodruff: Forms dense covers of attractive whorled leaves and, in spring, white flowers. It will tolerate the partial shade and full shade combination, and will tolerate dry conditions. It grows about 15-20 cm high.
Periwinkle: Not as dense, but more tolerant of deep shade. Deep green, shiny leaves; occasional blue flowers through the summer. About 15-20 cm.
Herb Robert: An annual or biennial that reseeds itself rather liberally. Can form dense covers year after year in dense or partial shade. About 20-25 cm.