Does this comply with building regs?

[ban-all-sheds]

Your assumptions are correct, although what your electrician has done is not illegal. It's a contravention of the regs, but regulations are just that, not law.

The law states that

Reasonable provision shall be made in the
design and installation of electrical installations
in order to protect persons operating,
maintaining or altering the installations from
fire or injury.

Since we can point to at least one instance of someone dying because of a cable not installed where BS7671 said it should be I think you're on a hiding to nothing trying to claim that installing a cable in the route shown in the photo constitutes "reasonable provision" for protecting people from injury.

Therefore it is illegal....