Clematis Armandii is rampant - mine has taken over the fence and a small tree in less than 2 years!! You do need a tall fence or additional trellis height for it though.. mine now has nowhere to go so I'm having to hack it back to keep it in order.
I also had a Solanum Glasnevin but again was too rampant for my fence so had to come out in the end.
Pyracantha might be an option - you can keep trained but some protrude up to 3ft beyond the top of a fence.
Fruit trees trained up a fence on wires can look really good and provide privacy but not evergreen. Also a climbing rose.
Wish I could find the perfect solution to this problem myself as my neighbours windows directly overlook our garden (sigh). I've resorted to planting cherry laurel for privacy and I'm slowly reducing the branches lower down so I get a standard shape eventually without losing too much border.