Eight men and one woman were arrested by Scotland Yard in a series of dawn raids on Thursday, the Met said in a briefing.
Police believe two of the individuals are linked but said all the offences are separate.
Some of them were living in hotels when they were detained, and the value of the frauds range from £25,000 to £100,000.
In response to the announcement, Shahin Sadafi, chair of Grenfell United said: "It is hurtful and saddening that people would take advantage of a tragedy like this.
"It is not just that they have taken funds and charity that was not for them, it is disrespectful to the real victims of the fire and people who lost their lives.
"Our community has shown strength, determination and dignity throughout the last year. Grenfell Tower was a community of good decent people, and we were proud to be each others' neighbours.
"These people have absolutely no place here. We are relieved they have been identified and rooted out."
More to follow.