Brand, 48, the former husband of US singer Katy Perry, worked on BBC radio programmes between 2006 and 2008.
He issued a denial on Saturday to unspecified "very serious criminal allegations" hours before the accusations of sexual assaults, including rape, were published online by the Sunday Times newspaper and later aired on Channel 4 television.
The Times and documentary show Dispatches reported that the alleged incidents had taken place between 2006 and 2013 and said one woman had made an allegation of rape, while another said Brand assaulted her when she was 16 and still at school.
Two of the accusers reported that the incidents occurred in Los Angeles, the paper said.
A BBC spokesperson said in a statement: "The documentary and associated reports contained serious allegations, spanning a number of years. Russell Brand worked on BBC radio programmes between 2006 and 2008 and we are urgently looking into the issues raised."
Banijay UK, the production company behind a television show once hosted by Brand, said it had launched "an urgent internal investigation".
"In light of the very serious allegations raised by Dispatches and The Times/Sunday Times investigation relating to the alleged serious misconduct of Russell Brand while presenting shows produced by Endemol in 2004 and 2005, Banijay UK has launched an urgent internal investigation," it said.
Women's charity Trevi, which helps women affected by violence and abuse, said it had ended its association with Brand, and Tavistock Wood, a talent agency, said in a statement it "has terminated all professional ties to Brand".
"Russell Brand categorically and vehemently denied the allegation made in 2020, but we now believe we were horribly misled by him," it said.
London's Metropolitan Police said it had not received any reports in relation to the allegations.
"If anyone believes they have been the victim of a sexual assault, no matter how long ago it happened, we would encourage them to contact the police," the police said in a statement.
