The announcement comes just a day after Abbey warned investors it would post its first loss next year, slash its dividend and cut jobs to counter the effect of rising bad debts which led to a profit warning in June.
Pople, 45, steps down from the Abbey board with immediate effect and his deputy John Berry will take over his responsibilities until Abbey finalises its new organisational structure.
"I am completely supportive of the new direction of the organisation, but after much thought I have decided that after six years running the retail bank I am ready to seek a fresh direction outside the group," Pople said in a statement.