The English comedian has been accused of pursuing audience members for sex while presenting Big Brother spin-off shows EFourum and Big Brother's Big Mouth on Channel 4, while other allegations relate to when he was a radio presenter for the BBC.
The claims were made in a joint investigation by The Sunday Times, The Times and Channel 4 Dispatches, in which four women make separate allegations of sexual assault.
Brand has denied the allegations.
A researcher claimed concerns about Brand's behaviour were reported to production managers at Endemol, the company commissioned by Channel 4 to produce the programs in 2004 and 2005, but were dismissed.
Following the publication of allegations against Brand, questions were being asked about whether TV chiefs were aware of any concerns about his behaviour while working on their programs.
Meanwhile The Times said it has been contacted by "several women" since publication with claims about Brand, but said their allegations have not yet been investigated and "will now be rigorously checked".
Channel 4 said in a statement: "We have asked the production company who produced the programs for Channel 4 to investigate these allegations and report their findings properly and satisfactorily to us.
"Channel 4 is also conducting its own internal investigation, and we would encourage anyone who is aware of such behaviour to contact us directly."
Banijay UK, which bought Endemol in 2020, said in a statement: "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 and will co-operate with any requests for information from broadcast partners and external agencies.
"We also encourage anybody who feels that they were affected by Brand's behaviour while working on these productions to contact us in confidence."
The BBC also said it is "urgently looking into the issues raised" while Brand worked on BBC radio programs between 2006 and 2008, having first appeared on BBC 6 Music in April 2006 before he was moved to Radio 2 in November of the same year.
The Metropolitan Police said it will speak to The Sunday Times and Channel 4 to ensure "any victims of crime who they have spoken with are aware of how they may report any criminal allegations to police".
A spokesman for the Los Angeles Police Department (LAPD) told the PA they do not have an open investigation into Brand, and another confirmed there had been no arrests following two allegations that are said to have happened in the US.
Brand, 48, was also accused of rape, sexual assault and emotional abuse between 2006 and 2013, when he was working for the BBC and Channel 4 and starring in Hollywood films.
The actor and comedian vehemently denies the allegations and, in a video posted online, said all of his relationships have been "consensual", before accusing the media of a "co-ordinated attack".
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