Al Fayed, who died aged 94 in 2023, took over the luxury department store in 1985 and sold it in 2010.
Of the 19 complaints, three were allegations of rape, 15 were sexual assault, and one related to trafficking.
The Met said it approached the Crown Prosecution Service (CPS) on five occasions between 2005 and 2023. No further action was taken in relation to any of the allegations.
It said it was “carrying out full reviews of all existing allegations reported to us about Al Fayed to ensure there are no new lines of enquiry”.
Officers are making contact with other organisations, including lawyers representing individuals whose allegations had featured in media reports, it said.
The Met said that, while there was no prospect of convicting Al Fayed himself, “we must ensure we fully explore whether any other individuals could be pursued for any criminal offences”.
Commander Stephen Clayman said: “It is vital that any victims have a voice and are able to report any allegations if they have not done so before, and know that they will be taken seriously.”
It said it had specialist teams in place and understood that for many years many people had sought answers.
The Crown Prosecution Service said it was “very concerning” that so many women are coming forward with allegations against Al Fayed, but added that when evidence against the former Harrods owner was first brought, “there was no realistic prospect of conviction and no charges were brought.”
A spokesperson said: “We are working to build a full picture around these serious allegations and want to reassure the public that alongside our criminal justice system partners, we are determined to secure justice in as many rape and serious sexual offences as possible”.
“If there are any future investigations relating to this matter, we will of course work in collaboration with police”.
Separately, Harrods’s managing director, Michael Ward, said earlier on Thursday that Al Fayed “presided over a toxic culture of secrecy, intimidation, fear of repercussion and sexual misconduct”.
He released a statement saying Harrods “failed our colleagues and for that we are deeply sorry”.
“We have all seen the survivors bravely speak about the terrible abuse they suffered at the hands of Harrods former owner Mohamed Fayed,” he said.
“While it is true that rumours of his behaviour circulated in the public domain, no charges or allegations were ever put to me by the Police, the CPS, internal channels or others.
“Had they been, I would of course have acted immediately.”
He said the “Harrods of today is unrecognisable to Harrods under [Al Fayed’s] ownership” and that the company had set up a settlement process for the victims.
Mr Ward also said he stepped back from his charity trustee positions while the review is taking place.
The Royal Ballet and Opera said in a statement Mr Ward resigned as a trustee from its board on Wednesday, effective immediately.
