Police from Scotland Yard have identified 38 people of interest including 12 UK nationals following a two-year review of evidence in the case. None of the 38 people identified are known to the McCanns.
Detective Chief Inspector Andy Redwood said his team has carried out new witness interviews and was in a "unique position" in analysing information from police in Portugal and the UK, as well as seven private detective firms.
He said: "That has given us the ability to see this case with fresh eyes, and through that bring out new, genuinely new, lines of inquiry. And I'm hopeful when we pursue those lines of inquiry that we will be able to bring some sort of resolution.
"Whether we will be able to solve it is a different issue, but I hope that we will be able to have the ability to move the investigation on.
"I believe critically that this is an important moment for Madeleine. It is the culmination of that unique piece of work and it is a great opportunity which we intend to exploit to the full."
Madeleine, then aged three, went missing from a holiday apartment in Praia da Luz in Portugal's Algarve on May 3 2007, as her parents Kate and Gerry dined at a nearby tapas restaurant with friends.
The Portuguese investigation is officially closed but authorities there are backing the Scotland Yard inquiry and officers from both countries will work together in pursuing new leads.
A team of 37 Met police officers and staff are working on the case, and they are sending a formal letter of request to Portuguese authorities for help.
The 12 British persons of interest were in Portugal at the time Madeleine vanished, and are currently thought to be in Portugal or the UK. The remainder are believed to be in these countries or three other unnamed European nations.
Mr Redwood said: "We and the Portuguese authorities remain completely committed to finding out what happened to Madeleine, and everything we do is utterly focused on her best interests.
"We continue to believe that there is a possibility that Madeleine is alive.
"It is a positive step in our hunt for Madeleine that our understanding of the evidence has enabled us to shift from review to investigation.
"We have identified 38 persons of interest from a number of European countries. Twelve of those people are UK nationals who we believe were in Portugal at the time Madeleine disappeared.
"Our working relationship with the Portuguese police is positive and now that we have moved to investigation we are requesting further specific assistance through normal judicial routes.
"We remain in close contact with Kate and Gerry McCann and they are updated on our current position."
So far the team has gathered 30,500 documents and generated 3,800 actions that they need to tackle.
They are around two-thirds of the way through their review, and so far have been to Portugal 16 times.
They have interviewed witnesses, found new evidence and are working on new theories about what happened to Madeleine.
Spokesman for the McCanns Clarence Mitchell said: "Kate and Gerry warmly welcome this shift in the Metropolitan Police emphasis. They see it as a huge step forward in establishing what happened and hope that it will lead to bringing to justice whoever was responsible for Madeleine's abduction."
If a British person were charged with a sexual offence or murder in relation to the case, then they could stand trial on UK soil.
While the investigation is at a very early stage, Mr Redwood said: "The review has given us new thinking, new theories, new evidence and new witnesses."
The senior detective said he "genuinely" believes that Madeleine may still be alive, and appealed to the public to keep looking for her.
"Over the last two years what the review has told me is that there is no clear definitive proof that Madeleine McCann is dead. So on that basis I still genuinely believe that there is a possibility that she is alive.
"I would ask the public to continue to look for her. If you look on the Metropolitan Police website you will see the image that we presented last year to the public and all the contact details.
"If the public aren't happy to talk to police then they can call Crimestoppers.
"Everything we are doing is focused towards trying to find Madeleine McCann. There are no guarantees of any outcome, but I can assure you of our absolute determination to try and establish what has happened to her."
He stressed that neither her parents nor the McCanns' friends who were having dinner with them that night are among the 38 people identified.
"Neither her parents or any of the members of the group who were with her are either persons of interest or suspects.
"They (the McCanns) are parents who have lost their daughter and we are doing all we can to bring resolution for them to find out what has happened to Madeleine."