Both the greater and lesser periwinkle are evergreen, widely used as groundcover and flower in spring/early summer. The flowers are normally blue-violet but I think you can get cultivers with white flowers and also variegated leaves.

Ivy is evergreen and is good for wildlife but often is disliked as it spreads too quickly. There are varieties with different leaf types - blueish, ones and variegated ones . I have used some to give all round cover near my pond but it is time to trim it to keep it in check now.

Pachysandra terminalis has attractive foliage and is used as a ground cover, and is evergreen.

Cotoneaster Coral Beauty is an evergreen shrub suitable as groundcover with whitish flowers in late srpring/early summer and orange-red berries in autumn.

Pleioblastus distichus and Pleoblastus pygmaeus are small bamboos that are often used as a ground cover.

Sedum is used as a very low ground cover in covering "living roofs" eg shed roofs in sunny places.

You can use conifers as ground cover too such as Cedrus deodara 'Feelin Blue' but they tend to be very slow to spread compared to other kinds of plant.

Gaultheria procumbens is another idea for a very low growing evergreen groundcover. I'm not sure if the flowers are that significant but the red berries are attractive in winter .

Leucothoe Red Leaf or other varieties of leucothe could be used - they are evergreen and some have very attractive red leaves in autumn and winter. I'm not sure how quickly they spread.

Depending on the size of ground cover you want, ( and soil type you have)there are some small azaleas and miniature rhododendrons that flower in spring and early summer that are evergreen and can also be used as groundcover.

You don't say whether in sun or shade - these tolerate shade pretty well: Ajuga reptans, Campanula muralis, Lamium maculatum varieties, Geranium macrorrhizum, Tolmeia (often in the houseplant section, but grows well in shade outside year round). There's a wide range of Geraniums (cranesbill types) that do well in dappled shade, and for full sun, the world's your oyster! Helianthemum, Arabis, Armeria, Pseudarmeria, Cotula hispida, Aubretia, Halimocistus, small Hebes such as H. 'Youngii', Oreganum aureum (herb section). All these plants have the advantage of spreading through the soil and covering the ground well (unlike Vinca!)

Thanks for all the information, I will go and check it out and see what I can plant!