grey area. personally I would either run SWA or in steel conduit, as mentioned above to stop accidental damage from hedge trimmers or rats chewing it. Depending on location low down on a fence should be ok. Have a think about if the fence is liable to storm damage and what might happen if a panel is blown down – hence why most clip to the gravel boards.
I am running power to the summer house this summer, consumer unit has an RCD but plan to use a secondary fused RCD as well. Rationale being any issues with the garden supply means I can just remove the fuse and the house will work fine. I plan to bury ours as we are also doing a patio at the same time
in the past I’ve had water ingress into an outdoor light, and it kept tripping the consumer unit until I finally worked out what it was and removed the light, being able to isolate circuits makes fault finding alot easier