English law recognises that there is a continuum between obviously employed and obviously self-employed, but the categorisation in any particular case will be down to the reality of the actual relationship between the employer/contracting company and its staff/contractors. There's no bright line, edge cases are ruled on case-by-case in the tribunal, as here.

The actual criteria are pretty complicated - see the guidance manual at https://www.gov.uk/hmrc-internal-manuals/employment-status-m... - but the essence of it is control ("does the boss have the right to tell the worker what, where, when and how to work?"), personal service/substitutability ("can the worker send someone else to do the job, instead of doing it himself?"), risk ("who is on the hook if something goes wrong?") and some other factors. Very fact-specific.

Incidentally, one of the standard features of traditional taxi drivers in the UK is that they don't set their fares, that being the responsibility of the local government. Uber drivers are licensed in the separate category of 'private hire', which has less stringent licensing (and the right for a firm to set its own fares) but a prohibition on picking up passengers by being hailed, and some other restrictions.