Woolfe was favourite to replace Nigel Farage as leader of the party but was hospitalised in Brussels earlier this month in an alleged fight with a UKIP MEP.
The BBC and Lucy Fisher, senior political correspondent with The Times, are reporting that Woolfe, also an MEP, has issued a statement saying the party is "ungovernable without Nigel Farage leading it and without the referendum cause to unite it." He is abandoning his leadership bid and resigning the party.
BREAKING: Steven Woolfe has quit Ukip, saying it's "ungovernable" without Farage & riven by "infighting, proxy wars". Full statement: pic.twitter.com/PHf4MPhaGW
- Lucy Fisher (@LOS_Fisher) October 17, 2016