The Trust has released a statement saying Maria Ball has resigned with immediate effect.
The process for appointing a new or interim chair will be started immediately but in the meantime Paul Remington who is vice chair will lead the organisation with Andrew Morgan, the interim chief executive.
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The father of a prisoner who electrocuted himself has welcomed the news specialist self-harm preventation training will be given to staff.
The Labour Party needs to accept the EU referendum result, and "move on", Justice Secretary Liz Truss has said.