The directors, led by Ed Warner, resigned after a hastily arranged general meeting.
"Following yesterday's peremptory, unconstitutional actions by the HCA chairs, my six independent director colleagues and I have decided to resign from the board of British Basketball with immediate effect," Warner said in a statement.
In May, the UK government's Department for Digital, Culture, Media and Sport granted 195,000 pounds ($259,000) to British Basketball for June and July fixtures. A further 305,000 pounds is guaranteed for international commitments in 2018-19.
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However, UK Sport said funds would be released only if British Basketball and the HCA could work together to find a sustainable financial and governance plan.
"It is very disappointing that the parties responsible for British Basketball were unable to reach collective agreement on the governance and the future financial sustainability of the sport," UK Sport said in a statement.
Warner said he had only faced "intransigence and aggression" from the HCA in his bid to find a solution to the financial challenges facing the sport.
"I cannot lead an organisation whose three members are so unwilling to work collectively, so devoid of ambition for the game, so full of disdain for Great Britain players and so apparently lacking in professional integrity," Warner said.
($1 = 0.7539 pounds)
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
