Anemones

I don't see why not. How wide is the space between the two walls? Things like aubretia, arabis, yellow alyssum, phlox and saponaria don't need a lot of earth to thrive in and they look lovely when they're tumbling over a wall. Then there are upright plants like sea pinks, ajuga reptans (bit of a thug but handsome), cyclamen, campanula, alpine scabious, all of which will give plenty of colour. Others will have suggestions too, I'm sure ?.

Your patio wall looks identical to mine!!

But the plants in mine are actually in the wall - it is a double wall with earth in between the two layers. Would alpines do well in there do you think? I do like the idea of colour all year round.

I have alpine at the back of my patio wall. You can have colour all the year round then. I also have a couple of helibores in there which flower in the late winter although it's possibly not the best place for them.