The claims were made in a joint investigation by The Sunday Times, The Times and Channel 4 Dispatches, and include allegations about controlling, abusive and predatory behaviour.
Brand was due to bring his Bipolarisation tour to The Halls next Thursday, and had been booked to perform in Windsor this Tuesday and Plymouth on Friday.
However, the show's promoters have now announced that all remaining dates on the tour have been postponed, saying: "We are postponing these few remaining addiction charity fundraiser shows, we don't like doing it - but we know you'll understand."
The Halls has shared this comment on their social media pages and said that all ticket holders will receive a full refund.
POSTPONED:— The Halls Wolverhampton (@TheHallsWolves) September 18, 2023
Statement from the promoters.
“We are postponing these few remaining addiction charity fund raiser shows, we don’t like doing it - but we know you’ll understand.’
All ticket holders will receive a full refund. More information will be available in the coming days. pic.twitter.com/h5NNHP30h6
The 48-year-old is being investigated by the BBC, Channel 4 and a production company after he was accused of rape, sexual assault and emotional abuse while working for the organisations.
The high-profile comedian and actor has denied the claims, including of controlling, abusive and predatory behaviour, which were made by four women relating to alleged incidents between 2006 and 2013 in the UK and US.
However, the Met Police has confirmed that it has also received an allegation of sexual assault in Soho, central London, in 2003.
The force said: "On Sunday September 17, the Met received a report of a sexual assault which was alleged to have taken place in Soho in central London in 2003.
"Officers are in contact with the woman and will be providing her with support.
"We first spoke with The Sunday Times on Saturday September 16 and have since made further approaches to The Sunday Times and Channel 4 to ensure that anyone who believes they have been the victim of a sexual offence is aware of how to report this to the police."
As Dispatches aired on Saturday evening, Brand appeared as scheduled at the 2,000-capacity Troubadour Wembley Park Theatre in north-west London to perform a sold-out comedy gig.
While not directly addressing the allegations, he reportedly said he hoped the audience would appreciate "there are obviously some things that I absolutely cannot talk about".
Russell Brand Bipolarisation was described on The Halls website as: "Rules and rule breaking! Democracy and freedom! We reach conclusions from mass confusion by polling the live audience. We want to hear YOUR opinion. After amassing a movement of 25 million people across his digital channels, the Community festival and the live show Stay Free; the cultural and political commentator and award-winning British comedian is back on stage."
Following the allegations made in Dispatches’ Russell Brand: In Plain Sight, the Trevi women and children’s charity in the UK said it had cut ties with Brand and his charity, the Stay Free Foundation.
On Brand’s website, the Stay Free Foundation is described as a charitable organisation that focuses on “supporting people through recovery from addiction, their mental health issues and the non-profit organisations that help them”.
It says it makes “regular donations” to treatment centres such as Friendly House in Los Angeles and BAC O’Connor in the UK, while also supporting the Trevi charity and the Treasures Foundation.
In a statement, the Treasures Foundation said it only knows Brand in the “the capacity of him wanting to make amends and give back to women”.
A statement added: “We can’t make an opinion on what has come out right now. We just know him for the good that he does now.”
Brand was rehabilitated from heroin addiction in the early 2000s and has since released his part personal memoir and part self-help guide titled Recovery: Freedom From Our Addictions, as well as setting up his Community festival, which sees all the profits donated to the Stay Free Foundation.
In the wake of the MeToo movement, Brand previously said he had no regrets about his earlier sexual behaviour, claiming to have had intimate relationships with hundreds of women in the past.
Brand was married to US pop star Katy Perry from 2010 to 2012, and is now married to Laura Gallacher, the sister of presenter Kirsty Gallacher. The couple have two children, Mabel and Peggy, with a third on the way.
In recent years Brand has seemingly become a prominent conspiracy theorist, using his YouTube channel with millions of followers to cover topical news stories, including alleged misinformation surrounding the Covid-19 pandemic and being an outspoken sceptic of vaccination.