LONDON (Reuters) - Ex-News Corp executive Rebekah Brooks will give her full cooperation to British government and police inquiries and a parliamentary hearing scheduled for next week, she said in an internal memo.

Brooks, who was editor of the News of the World tabloid when it hacked into voicemail messages of murder victims and bereaved relatives, quit despite strong support from News Corp Chief Executive Rupert Murdoch, the company said on Friday.

"I have given Rupert and James Murdoch my resignation. While it has been a subject of discussion, this time my resignation has been accepted," she wrote in a message to staff.

"My resignation makes it possible for me to have the freedom and the time to give my full cooperation to all the current and future inquiries, the police investigations and the CMS (parliamentary committee) appearance.

(Reporting by Georgina Prodhan, editing by Julie Crust)