Agreed, there should be an exemption for part-time work. Why is there a gulf between "unpaid" and "minimum wage" - what if someone wants to just ride the bike for fun and make a couple of pounds as a bonus?
Minimum wage laws are there to prevent exactly this scenario. It is deemed better to let inefficient enterprises that cannot pay even minimum wage to implode and support unlucky people via government programs rather inefficient enterprises.
Unravelling worker rights is just a race to the bottom.
Are we just now rediscovering why minimum wages are bad?
Edit: Any skeptics don't have to trust me, they also have the option to trust the International Labour Organization:
https://www.ilo.org/global/topics/wages/minimum-wages/settin...
But there are some sectors (building, cleaning etc.) that do have a government set minimum pay, because they often would exploit foreign workers.
Actually, our foodora bicyclists a while back formed a union, striked, and got a tariff deal. So got rid of some of the problems around their gig-work.