Check out Escallonia. That might fit the bill, although you won't get as many flowers on the part in the shade.

I think Pyracantha might also be OK, though, as I have one facing north which flowers and berries well.

You may be struggling to find much that will grow to 6 feet tall and flower in full shade if there really is no direct sunlight ..

Ivy's are the obvious answer to full shade and will grow up a fence but obviously they don't have showy flowers.There are some lovely variegated versions and some which are very light green or yellow

Shrubs that will cope with shade are

Choisya( white flowers ,evergreen)

Aucuba( insignificant flowers but has berries ,evergreen)

Cotoneaster( white flowers,red berries.. some are evergreen)

Euonymus fortunei ( slow growing but will eventually reach 6 feet or more , no berries or flowers,

Hydrangea, flowers but not evergreen ,

mahonia ,yellow flowers ,evergreen

osmanthus burkwoodi,white flowers,evergreen

cherry laurel(prunus laurocerasus) - white flowers -evergreen

pyracantha- evergreen red or yellow berries

viburnum tinus - white flowers,black berries,evergreen

I'd add Elaeagnus varieties to the list of shrubs which tolerate shade pretty well - lots of colourful options in that group, evergreen, variegated leaves.

Thank-you for your great advice, I have somewhere to start researching from - I appreciate your suggestions. David.