It is happy to act aggressively against management it thinks are failing. Tosca made a tentative bid for TalkTalk last year at the much higher price of 135p a share, around £1.5 billion.
TalkTalk is being advised by Barclays and Deutsche.
Toscafund has until November 5 to formalise its bid, but the deal could be done well before then conditional on the support of Dunstone.
City analysts think a rival bid, perhaps from Vodafone, is a possibility.
Private equity firms, awash with cash, could also be interested.
Toscafund previously bought telecom firm Daisy Group, taking it private in 2015.
Hughes was a banking analyst who later worked at US hedge fund Tiger before setting up Toscafund in 2000.