Shereef Abdallah, who boasts he can make up to £150 an hour posing as the Labour leader, is said to have made the slurs on the social network site Twitter.
The woman, known only as Rachel, complained to police after he branded her a “Zionist bully”. Malaysian-born Mr Abdallah, who has worked as a volunteer for the Labour MP Glenda Jackson, is also accused of stalking and threatening a student, Julie, 24.
She said: “He started to get very personal, very abusive and very intimidating. Just after Christmas he threatened to kill me and that is when I decided to contact the police.”
Mr Abdallah lives with his parents in north London. Records show he has made nearly 17,000 tweets since last July, most of them to just four people including Julie and Rachel, 32.
Rachel, who challenged him for using the offensive term, has been called a Nazi, “Zionist bully” and “warmonger”.
Rachel was last night too frightened to comment but Julie said: “His tweets are very creepy. He seems to hate women who have an opinion.”
Mr Abdallah denied sending abuse or death threats and said: “I had a debate with someone called Julie on Twitter about the Iraq war last November.
“She became very abusive and labelled me a jihadist. Others, including Rachel, have also abused me and threatened my life but the police told me there was nothing they could do.”
Last night the Metropolitan Police confirmed they were investigating an allegation of malicious communication.
A spokesman for Ed Miliband denied that he knew Mr Abdallah. The Labour Party has suspended Mr Abdallah’s membership