MET Commander Paul Brogden said on Wednesday that after revision, the MET had concluded that the investigation was no longer proportionate.
"It is the duty of police to assess and, if appropriate, fully investigate alleged offences and the public would expect us to investigate an allegation of this nature," Brogden said.
"We conducted initial inquiries to establish the full circumstances and sought early advice from the CPS. Having had the opportunity to review this, it is no longer proportionate that this investigation continues.
He said the MET had "made direct contact with the individuals involved and updated them on this decision."
Starkey said in response that the investigation should never have begun.
"I'd like to thank all of you for your support, especially those who dislike my politics but recognised the dangerous precedent this case set," his tweet reads.
"I'd especially like to thank @SpeechUnion and @LukeSGittos1986 for their tireless work in seeking to defend freedom of expression," he added.
Grimes said that he would continue to seek answers on how the investigation was allowed to begin in what he described as an "unprecedented use of the Public Order Act to regulate speech & debate," and that he would "campaign to ensure the precedent the police have set with this investigation doesn't put free expression at risk."
During a heated discussion about “the scholarship behind the laudable slogan of Black Lives Matter, compared to the movement seeking to delegitimate [sic] British history,” the historian said "slavery was not genocide, otherwise there wouldn’t be so many damn blacks in Africa or in Britain."