It's natural - you still have to be licensed with tfl to drive uber; all minicab drivers were already licensed; uber is a better platform to drive for than a shitty call-in minicab company. So most of the drivers switched, and only people who have got licensed after uber showed up don't count as 'used to be minicab driver's.
Why is the license a good idea? because it stops rapists posing as taxi drivers (which alas is still a problem even with prominant signage.)
Uber only provides a customer gateway, there are may other out there.
For those of you in the US, the important thing to note is that the market is much freer than say new york, there are only two requirements:
1) a safe car
2) a minicab license (https://tfl.gov.uk/info-for/taxis-and-private-hire/licensing...) which is reasonably cheap.
As a customer, I'm happy with that level of regulation.