Channing, who is believed to be freelancing as a director at MWW after leaving Uber at the end of September, was responsible for bringing in PR agency Burson-Marsteller in June to help Uber handle the media attention it attracted following protests by London black-cab drivers.
Burston-Marsteller was then appointed for a long-term EMEA brief, taking over from Westbourne Communications. Westbourne continues to look after UK public affairs for Uber.
Ben Novick, senior comms lead EMEA at Uber, will take over from Channing for the time being.
It is understood that Moxon-Tritsch, who joined Uber in February this year as head of EU policy, left in the middle of this month.
In September Uber brought in Mark MacGann, the former leader of Weber Shandwick's EU public affairs practice, as head of public policy for EMEA. MacGann left NYSE Euronext after four years in May.
The company also has the manager of Barack Obama's 2008 US presidential election campaign, David Plouffe, managing all global policy and political activities, communications, and Uber branding efforts. Plouffe was hired in August by Uber CEO Travis Kalanick.