TfL won't issue rideshare driving licences, you've got the erm end of the stick there. The city struggles to cope with the congestion UberX causes. Unrecorded earnings would be more of a problem with "traditional" PH firms than with Uber. Like mytaxi, Uber documents every job and every penny every driver collects. In fact, if that is their problem, Uber is their solution.
Leo might have the answer, erm. According to Joe Heron the 20,000 reduction in taxi driver numbers over here since 2009 is down to drivers finding better paid jobs. Seems that we need 20,000 men willing to drive drunks about for little reward.