It depends a lot on the driver:
If a person has a full / part time job in another business, but is prepared to pick up and drop off an Uber client as part of their journey, and reap the benefit, then that is equivalent to car sharing, and they are clearly not an employee in any meaningful sense.
However, if someone's main income is derived from driving around picking up and dropping off Uber clients, then they are acting as an employee.
In addition, in the latter case, they are clearly using their car "for the purposes of hire or reward", and therefore a normal car insurance policy won't cover them, and they should have a commercial insurance.