If you have a south or west facing and slighly sheltered place for it, then Solanum laxum 'Album' fits the bill. It has clusters of beautiful white flowers in the summer through until the frosts.

Otherwise, try a Honeysuckle. There are plenty to choose from, some being scented.

Neither's evergreen though, are they Spritz?

I have evergreen Honeysuckes??? (not all though!) I suppose my Solanum could be classed as 'semi-evergreen' in a normal year, Bamboo!

I was thinking Jasmine officinale, but that isn't evergreen unless it's a mild winter.

This Guest is in Hampshire - would you class the general area as mild-ish, obviously depending on the specific location of the garden?

Think Hampshire's like Surrey - has some very cold spots, so hard to say, but technically it should be "soft" in weather terms.

I'm a bit stuck - fast growing evergreen climbers...Roses?? I know you don't like them, but Guest might!! :-))