Labour MP Kate Hoey, who is a member of Labour Leave, has quit Vote Leave, but will continue to support Grassroots Out, another Out campaign group.
Labour Leave will also end its affiliation to Vote Leave, according to the BBC.
The outbreak comes after Mills, a Labour donor and deputy chairman of Vote Leave, warned about "damaging bickering" at the top of the group. Mills added that infighting within Vote Leave had prompted the Hoey's departure.
Meanwhile, leader of the UK Independence Party Nigel Farage said during his LBC phone in that Vote Leave "refuse to work with anybody".
Co-founder of Leave.EU Arron Banks has also criticised members of Vote Leave. "It is now crystal clear that they have zero interest in joining forces," he said.
Both Vote Leave and Leave.EU are competing to be chosen by the Electoral Commission as the official side that will be entitled to broadcast campaign speeches, receive a publicly funded grant of up to £600,000 and send a leaflet to each household.
Conservative MP Tom Pursglove, who is a member of Grassroots Out tried to calm the tensions, having said: "It can't carry on as we are. We need to focus on winning the referendum."
Pursglove has not ruled out the possibility of Grassroots Out also vying to become the official Out side.