The force’s promise comes after a Channel 4 investigation found that more than half a dozen allegations had been made against her and her former boyfriend Jeffrey Epstein.
The alleged UK-based crimes - which include trafficking, grooming, sexual assualt and rape - span a period of more than a decade.
Maxwell is currently in a US prison charged with aiding Epstein’s sexual abuse between 1994 and 1997, while he was found dead in his prison cell on 10 August 2019.
Channel 4’s findings were based on interviews, witness accounts and publicly available documents.
They put pressure on the Met Police, which decided in 2016 not to launch a full criminal investigation into an incident involving Epstein, Maxwell and Prince Andrew in 2001.
Explaining its decision, the force said it was “not the appropriate authority” to investigate the charge of human trafficking because most of the activities reportedly took place outside of the UK.
Nazir Afzal, the former chief prosecutor for north-west England, has seen the latest evidence and believes the police must look into the claims.
He told Channel 4 News: “From what I’ve seen, there is clearly enough evidence for the police to investigate more thoroughly than they have done up to now.
“It’s concerning, because we’ve got potentially victims here. And maybe other victims or alleged victims who may, if an investigation follows its course, be identified.”
Mr Afzal also suggested that the police might have taken a different approach if Epstein and Maxwell had not been linked to Prince Andrew.
“The perception here is a different approach was taken in relation to these alleged offences, then there would be than if it was some brown guy in Rochdale, or some sex offender in London who didn’t have any standing at all,” he said.
The Met Police was directly approached by one of the alleged UK victims in 2016 but no action was taken, according to Channel 4.
In a statement, the force said it took reports of sexual offences and exploitation seriously, adding that it would investigate claims where there was sufficient evidence.
It added: “The MPS has continued to liaise and offer assistance with other law enforcement agencies who lead the investigation into matters related to Jeffrey Epstein but is unable to comment on individuals with whom they may or may not have interacted with regard any allegations of crime.
“We will always consider any new information and will review the information sent to us from Channel 4.”