The Metropolitan Police said a BBC Crimewatch appeal to be aired on Monday would feature “the most detailed reconstruction” of the case yet.
It will also broadcast e-fits of a number of men police want to find, the BBC is reporting today.
The McCanns Donegal relatives will be watching anxiously, hoping this could be a massive breakthrough in the case. Madeleine visited Donegal with her parents Gerry and Kate just a few weeks before she disappeared in Portugal in May 2007.
Portuguese authorities dropped their investigation into the case in 2008, but Scotland Yard started a review in May 2011.
The BBC says the purpose of the Crimewatch appeal, which police are describing as the “most complex and detailed” so far in the case, is to try to identify a number of computer-generated images, or e-fits, of men who were sighted in and around Praia da Luz on or before Thursday 3 May 2007.
As part of that effort, a reconstruction – almost 25 minutes long – of events leading up to and surrounding Madeleine’s disappearance will be shown.
Det Ch Insp Andy Redwood, who is heading the investigation, said: “The timeline we have now established has given new significance to sightings and movements of people in and around Praia da Luz at the time of Madeleine’s disappearancel
“Our work to date has significantly changed the timeline and the accepted version of events that has been in the public domain to date.
“It has allowed us to work with Crimewatch to build the most detailed reconstruction as yet, and highlight very specific appeal points.
“I hope that when the public see our investigative strands drawn together within the overall context of that appeal, it will bring in new information that moves our investigation forward.”
DCI Redwood said that police had sought to “try and draw everything back to zero… take everything back to the beginning and then reanalyse and reassess everything, accepting nothing”.
He added: “The careful and critical analysis of the timeline has been absolutely key. Primarily, we are focused on the area between 8.30pm and 10pm.
“We know that at 8.30, that was the time that Mr and Mrs McCann went down to the tapas area for their dinner, and we know that at around 10pm, that was when Mrs McCann found that Madeleine was missing.”
Madeleine’s parents will make a live appeal in the studio during the programme and, ahead of the broadcast, they told the BBC how much they still miss her.
“When it’s a special occasion, when you should be at your happiest, and Madeleine’s not there, that’s when it really hits home,” Mr McCann said.
Mrs McCann added: “It’s when you have the big family occasions… and you haven’t got your complete family.”
Earlier this month, police said phone records may be key to the case after it emerged officers were analysing data from phones belonging to people who were in Praia da Luz when Madeleine vanished.
The Crimewatch appeal, which will be shown in the UK on BBC One on Monday from 2100 BST, will also be broadcast in the Netherlands and Germany.
Madeleine in Donegal, pictured second from left in April 2007. She disappeared in Portugal two weeks later.