The website quotes a Lib Dem source as saying: “This may be the speech that John Hayes and the Tory Tea Party wanted but it wasn't even delivered because he was told not to.”
Mr Davey allegedly vetoed key lines from Mr Hayes’ speech after seeing its first draft.
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Five people have been killed and 40 injured after a car and knife attack in London on Wednesday.
A wet, wintry night in places with rain and hill snow slow to move away from southern Scotland and northern England.
The Westminster terror attack dominates the front pages of Thursday's newspapers.