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It's possible that drivers are rat running, but there are a lot of restaurants in that area and Exeter St/ Tavistock St is one of the few ways to enter the South part of Covent Garden for deliveries.
Obviously that doesn't excuse shit driving.
Until there is a system for co-ordinating all the commercial, daily deliveries to that area it will always be shit for pedestrians and cyclists during the morning rush period.
There must be a better system for that bit but I don't know what. It's always a shit show, with peds and vehicles.