Jim Gamble, the former head of the Child Exploitation & Online Protection Centre (Ceop), also said that so many agencies from the UK got involved, it damaged relations with Portuguese police.
Within weeks of the three-year-old going missing from Praia da Luz in May, 2007, Ceop, the Metropolitan Police, the Serious Organised Crime Agency and the National Police Improvement Agency all intervened, creating "resentment" among Portuguese officers, his report found.
Mr Gamble's report was commissioned by former Home Secretary Alan Johnson in 2009.
He said Britain was warned not to behave like a "colonial power" after challenges to the early investigations by Portuguese police.
Mr Gamble said: "When this [the disappearance] happened your first gut reaction is that you want to help, a child has gone missing.
"In Ceop we were no different than anyone else.
"So there is this rush to help in the early stage and I think because the UK did not have a structure for dealing with this ... so everyone came with best intention, that created a sense of chaos and a sense of competition.
"I've no doubt relationships from the outset with the Portuguese were impacted by it and I think that had a long-term negative effect on the investigation."
The Home Office, which declined to release the report under Freedom of Information laws, has not responded to requests for a comment.
Policing Minister Mike Penning said the Government remained "fully committed" to supporting the search for Madeleine.
He said: "That is why, in response to this operational review, we asked the Metropolitan Police to take forward their current investigation."