Brand has strongly denied accusations made by four women in an investigation by The Sunday Times, The Times and Channel 4’s Dispatches.
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.
Police said in a short statement that all allegations were non-recent.
The force also said that 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.”
All women who have made allegations will be offered specialist support by the force, it said.
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”.