Re: I know many people who work so-called "gig economy" jobs here in California.
Contracting to multiple service providers is a problem if three of them want to set your hours to overlapping times - see there's no difference. If your terms of employment or contracting allow you to pick your own hours (as I believe both Uber and Lyft do), then it matters not whether you are contracting to them or employed by them.
UK or California law - makes no difference to the fundamental problem (or non-problem) you bring up.