London's Metropolitan Police said that investigators have been able to "place more significance" on events the night the then-3-year-old vanished from a Portuguese resort in May 2007.
Det. Chief Inspector Andy Redwood says Scotland Yard's investigation has "significantly changed the timeline" and accepted version of events of that night.
He did not elaborate on what has changed, but said he hopes when the public sees the new reconstruction more information will come in that will move the investigation forward.
Police said they would like to identify the men and eliminate the innocent as suspects.
Since launching its own investigation, 41 people of interest have been identified by Metropolitan Police, including 15 UK nationals.