One thing worth noting is that the UK is already a little different from the US, because Uber drivers are required to have a private hire license issued by the city where you're operating.
For example, in London you'd be required to have a full criminal background check, a medical examination, and pass a "topographical skills check" (basic route planning and map reading).
So it wasn't like you could just apply to Uber and be up and running within a few days to begin with.
From the way some of the drivers manage some trips I've been on, I'd say that was definitely the case ahaha
I would be happy for such innovation in contract law if the provisions to protect citizens were less tied to employment.
I too will be interested to see how this plays out, as I think Uber would still need to stay to maintain market position, lest they end up losing UK to a competitor. But as you point out, it will certainly make them likely to be more picky in "hiring" new drivers.
I wonder if it will be a net positive for workers or not in the short and long term.