Ivy seems an odd suggestion on the basis that it has proved to grow well where the soil is extremely dry, given the inclusion of damp slope in the Title. Hedera helix (there are other ivies) can make a nuisance of itself in many settings but it does prefer the soil it lives in to be well-drained.
However Phacelia may be an even stranger suggestion if the question is anything like my interpretation of the requirement. For Phacelia GrowVeg recommends:
Any sunny site with good drainage.
Full sun to partial afternoon shade.
Phacelia seedlings can tolerate light frost, but the plants are easily damaged by hard freezes.
"shaded hillside" and "can easily hit -5C" are at odds with the above.
The (rather limited) conditions mentioned by OP include shade, moist and ground cover and selecting "Sunlight: Partial", "Moisture: Moist but well-drained", "Planting places: "Banks and Slopes", "Hardiness: H3", "Habit: Mat forming" and "Native to the United Kingdom" at the Royal Horticultural Society plant selection site, returns only one result, Fuchsia procumbens. Although the OP has not mentioned soil type or pH, this plant can be comfortable in Sand, Chalk, Loam, Clay whether Acid, Alkaline or Neutral (RHS).
Other details that might have helped are aspect, exposure and time scale. For "lock the soil" it might have to be a case of choosing priorities - plants that provide ground cover quickly generally have shallow roots.