How are cabs even relevant at all to the point your original post brings up?
"Indeed if TfL have any kind of ulterior motive for their actions, it is simply that they dislike the impact Uber are having on congestion within the capital"
I.E. Uber is adding a mass of cars to the street and worsening congestion, likely by offering cheaper fares and tempting people off busses and the tube.
Surely Black Cabs aren't relevant to that point?