Dominic Cummings was sort of the communications director, but the leading political figures in Vote Leave were Euro-sceptic members of the Conservative party and the Labour party. Boris Johnson and Michael Gove were the political figureheads of Vote Leave when the referendum was called, but the executive leadership, as it were, came from people like Matthew Elliott and Dominic Cummings.
On May 3rd, 2018. See this statement in context.