LONDON, May 22 (Reuters) - Prominent Brexit supporter Andrea Leadsom resigned from British Prime Minister Theresa May's cabinet on Wednesday, saying she could no longer support the government's approach after May's latest gambit to pass her Brexit deal backfired.

"I no longer believe that our approach will deliver on the referendum result," Leadsom, who served as Leader of the House of Commons, said in a resignation letter to May.

"It is therefore with great regret and with a heavy heart that I resign from the government." (Reporting by Alistair Smout; Editing by Catherine Evans)