The MEP said: “I think they”ve got a spiral, someone suggested that it”s a death spiral, of their own making.
“I think unless someone very quickly can wrestle with the issues that they”ve got then we will see the loss of something that I think shouldn”t be lost.”
Mr Woolfe had been running to be the next leader of the party, after Nigel Farage”s replacement Diane James resigned soon after taking control.
He also warned the “elites” will make “great efforts to prevent Brexit”.
Mr Woolfe, who had been the front-runner in the leadership race, said: “There is just this visceral hatred towards Nigel or anyone who is seen to be associated with him.
“Some people call me his puppet for standing, things like that.”
He was hospitalised earlier this month following an alleged altercation with fellow MEP Mike Hookem.
While Mr Hookem has said no physical confrontation took place, Mr Woolfe said today: “He rushed at me. A blow to my face forced me back through the door.”
Ukip donor Aaron Banks is also now believed to be considering withdrawing his funding for the party.
The party will announce its new leader on November 28.