Multiple mayors - including the current PM who was once Mayor of London - have explained that there needs to be an open culture.
There are other private hire vehicle operator firms in London. Addison Lee is huge, and there are many, many "minicab" firms. They all comply with TfL's licensing and vetting procedures. Uber does not.
This isn't "black cabs vs Uber", this is "black cabs, Addison Lee, all the minicab firms, TfL and the Mayor of London demanding basic vetting procedures that everybody else does without question or issue".