Davison, who has been with the paper for six years, is the 10th high-profile journalist to leave the paper since Wadley took over from Max Hastings at the beginning of year. She is not thought to have another job to go to.
Executive editor Guy Eaton, a former long-time Daily Mail journalist who Wadley brought with her when she moved from the mid-market tabloid to edit the Standard, has been promoted to features editor.
Davison is the latest in a long line of journalists to leave the paper since Wadley joined.
This month, managing director Sally de la Bedoyere quit after 17 years at the paper and Jeremy Langmead, editor of the Standard's Life and Style supplement, quit to become editor-in-chief at IPC Media's style bible Wallpaper.
In July, astrologer Sarah Bartlett was told her freelance contract would not be renewed.
May saw the departure of Nicola Jeal, assistant editor (features), who left without a job to go to. Deputy City editor Joanne Hart was given three months' notice after nine years at the paper and Jo Revill, a Standard journalist, left to become health editor at The Observer.
In February, interviewer and features writer Andrew Billen and media editor Vincent Graff left to join The Times, while sports editor Mick Dennis left and has since got a job at the Daily Mirror.
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