Evergreen Climber

Passion flower is nice, keeps its leaves in winter but does get a bit straggly looking. Freshens up again early summer. Great flowers, interesting fruits afterwards.
Clematis armandii is a lovely evergreen, flowers in Feb/Mar though.

As I do not know which part of the UK you live in, it is a bit tricky to advise you. But if you are not in too cold an area, you might try abutilon megapotanicum. This is not really a climber and will need tying to the trellis but will make six feet each way - mine flowered right the way through last winter and is still going strong in mid July!
Another possibility in the south is a solanum. This could reach 20 feet but a bit of gentle persuasion and the occasional chop of tall shoots during the growing season will keep it in bounds. I also reduce it by about two thirds in Spring and it doesn't mind at all

Marguerite - my Jasmine goes bare in winter! As does my solanum Andrewr! My Passion fower retains more leaves....on the trellis out front, obscuring the road. Bought an evergreen climbing fern the other day, but no flowers of course.