LONDON— BP’s ousted chairman clashed with a fellow director earlier this year over the handling of sensitive talks about a potential deal, a sign of simmering boardroom tensions months before Albert Manifold’s abrupt dismissal this week. In private conversations, Manifold accused nonexecutive director Simon Henry, a former finance chief of BP rival Shell, of overstepping his authority and cutting other board members out of communications, according to people familiar with the dispute.  Henry denied any mishandling of talks, the people said. He argued that Manifold was mischaracterizing conversations among directors, executives and BP’s internal deals team, and needed to listen…