No need for Building Regs. involvement, as stated, it’s under 30m²m. And not habitable (were it habitable, the 30m² rule wouldn’t apply anyway).
On the electrics front, use a Part P electrician, it is the easiest way.
You can still DIY electrics, far more than people realise, but anything outside the main dwelling or in a ‘special location’ (kitchen/bathroom) is covered by Part P.
You can extend & modify existing circuits (provided they aren’t in special locations, as above), without instigating Part P, and most local authorities accept applications for electrical works if you don’t want to use a Part P registered electrician. We request a wiring diagram, inspect 1st fix visually, and get an electrician in to test the circuits on completion. Costs about £200, but there is a limit on the no. of circuits.