That doesn't really matter. Nor is it really true, since you inevitably interact with the driver. And it's understood that drivers are humans, and they are different.

McDonalds operates a franchise, you got the same thing, but still, different companies.

Yes, Uber had not structured itself as a franchise, but the use of [sub]contractors to provide a service with a controlled and sort of guaranteed (and well marketed and branded) quality - in itself - doesn't make the drivers employees.

I think the line between contracting and employment is up to the host society to draw.

Usually tax authorities have a few simple rules and if you are in compliance of at least half of them (or if you break at least X of them), then you are a contractor (or disguised employee). For example exclusivity is important here, the rule states that if a contractor gets more than 50% of its income from one entity, then that's one strike (and there are 5 other rules).

Of course it seems in UK law the drivers have standing, so it means there must be some statute about when a contractor is to be treated like employees. (For example, let's say you can't use temp workers, contractors like regular full time employees and not give them free cafeteria, if your regular employees have that perk.)