The newspaper reports it is the first time the Liberal Democrats have slumped to fourth position in one of its polls, and suggests the allegations regarding Lord Rennard may have hit the party's popularity.
The poll was conducted between Friday and Sunday soon after news of the allegations emerged.
The result comes just days before the Liberal Democrats attempt to defend the Eastleigh seat vacated by former Energy Secretary Chris Huhne.
Nobody thinks Nick is the kind of guy who would defend a 'boy's club', but that does not necessarily mean he has handled the issue well.
One of the women who made allegations against Lord Rennard told ITV News that Lib Dem leader Nick Clegg shifted his position on the matter.
Questions for the Lib Dems mount, centred on what senior members knew about allegations surrounding former chief exec Lord Rennard and when.