Very dry, sandy, sunny, narrow border

Hello. Can anyone recommend plants which would love my very dry and sandy, root-filled, nutrient-deficiant, narrow border? The border is next to a 3ft tall South-West facing fence which receives mostly full sun from late morning to about 6pm. The border is only about 18 inch wide and about 15 ft long. I would prefer plants that give height rather than spread because the border is right next to a narrow pathway. I would be particularly interested in plants which grow to about 5 ft to help give a little privacy through summer until the first frosts. There is no trellis on the fence and any support would have to be provided with canes etc.
I would prefer not to have to improve the soil if at all possible for a number of reasons (mostly a lack of money).
Also, I have a dog who likes to eat fruit from my garden so I have to be careful with toxic berries etc.
All advice gratefully received, thank you
Posts
Can I get some blith please Verd?

Good suggestion there although I wouldn't use Choisya in such a narrow border. Although you say you want some height, that would be tricky given the dimensions, but if you can attach some wires on vine eyes on the fence, you could have clematis or other climbers along your fence to give you height. Just make sure they have good nutrition when you put them in. Alliums will also add height and will like those conditions.
I live in west central Scotland - not where that photo is...
Wow, thank you everybody! I thought I was asking for the impossible but it seems not. There CAN be life in my difficult border after all! I'm going to have a look on the tinternet at the plants (and links) you've recommended...I may be some time
Thanks again!
Tall vertical plants that aren't very wide at the base are also good to give some height. If its a very sunny and warm position why not consider bulbous plants like Agapanthus and Foxtail lilies (Eremurus)?
Thanks Hippophae!
Happy hunting for the right plants Happyflower