Leafster, I am going to boringly suggest clematis...mostly evergreen. Woodbine (honeysuckle) is indeed a woodland plant and will be desperately unhappy in the conditions you describe...but traditionally, clematis very much like their heads in the sun while their roots are shaded (and usually a concrete or stone slab put over them). The most obvious choice, if you are wanting coverage, is c.armandii...but try to look for the smaller, more mannerly varieties, rather than the true species or varieties such as 'Avalanche'. I believe ClematisOnline sell 'Little White Charm' - the most beautiful evergreen. Mostly, the evergreen clema (cartmannii, cirrhosa, armandii, uruphylla and tangutica) are all winter or early spring flowerers...but what a show they generally put on. The armandii are also beautifully fragrant.
I was going to suggest tracleospermum...but they like the sun and are painfully slow.
Avoid the montanas. They are not evergreen and will leave a tangled mass of wood which are fine when stashed behind a shed but horrible, when on show for the rest of the year.
Talking of clematis, one of my favourite species, c,recta is in full, frothy growth at the moment. I despise those large flowered clems but absolutely love the smaller species, along with nodding viticellas and texensis...and especially, the fragrant autumn flowering terniflora and flammula. Clems - truly a flower for every month of the year.
O
iona - I feel your pain. I am detesting my garden at the moment. The massive ceanothus, box and euonymous have robbed all the sun and I feel like I am standing in a lowering corridor, barely held in control. All creeping in from the other side too - a whopping lemon verbena, kirengoshoma and chaenomeles have resulted in all my little beauties being squashed in their pots, overlooked by verdant, but oppressive greenery. Much worse after I visited a friends gorgeously open and sunny garden yesterday.
I am struggling to justify ripping out entire trees, huge roses and giant lilies but yep, feeling hateful and oppressed. Everything is so bloody huge - even the scented leaf geraniums are 3 feet. and I now have too many shrubby salvias....O, it just seems hopeless.