The comedian and actor has strongly denied accusations made by four women in an investigation by The Sunday Times, The Times and Channel 4's Dispatches.
But on Monday, the force said they have since received a “number of allegations of sexual offences in London" as well as elsewhere in the country.
In a short statement, police said all allegations were non-recent and there have been no arrests.
Detective Superintendent Andy Furphy, from the Met's Central Specialist Crime Command, said: “We continue to encourage anyone who believes they may have been a victim of a sexual offence, no matter how long ago it was, to contact us.
“We understand it can feel like a difficult step to take and I want to reassure that we have a team of specialist officers available to advise and support."
Claims were first made against Brand by four women earlier this month, who alleged sexual assaults between 2006 and 2013, while he was a presenter for BBC Radio 2 and Channel 4 and then as an actor in the US.
The Met previously said it had received an allegation of sexual assault in Soho, central London, in 2003, which emerged as the remaining live shows for his Bipolarisation tour were postponed.
On Saturday, Brand thanked his supporters for “questioning" the allegations of rape and sexual assault made against him.
In the three-minute clip, posted on YouTube, Rumble and X, he said the week since the claims were published had been “extraordinary and distressing".
Shortly after the Met issued its short statement on Monday, Brand made his first return to his regular Rumble show since the allegations were made against him.
The online video platform which refused to follow YouTube in blocking the comedian from earning advertising revenue on its site.
Brand said he would talk about the "collusion between big tech and Government and an apparent concerted effort by legacy media ... to silence independent media voices".
He added: "Obviously, it's difficult for me to be entirely objective given the events of the last week, but that's what we must try to do."