The main argument black cab (taxi) drivers are making is that Transport for London (the regulatory body) forces them to go through a bunch of extra steps before they can work (1) whereas minicabs (e.g. Ubers) are free from this.
That said, it's definitely a good thing these measures did not pass because they simply made minicabs worse rather than trying to improve the situation for taxi drivers whose "it's unfair" argument is a valid one.
Even as someone who is open to new tech, there are nuanced arguments on both sides which are often overlooked.
(1) For example, taxi drivers must do a navigation test learning the vast majority of roads in London ("The Knowledge"); be CRB checked where minicab drivers do not.