Kate and Gerry McCann hold an age-progressed police image of their daughter Madeleine during a news conference, May 2, 2012, in London. (Dan Kitwood/Getty Images)

LONDON - British police have begun to pour through 39,148 documents containing data collected from thousands of mobile phones to solve the case of Madeleine McCann.

The British girl disappeared while on a family holiday to Portugal in 2007, just days before her fourth birthday, and her case has become a national obsession in the United Kingdom.

Detective Chief Inspector Andy Redwood, who's heading the inquiry, told the press in a briefing on Thursday that police were going through a "substantial amount of data" obtained from cell phones belonging to people staying in the Praia de Luz resort, where the McCanns were vacationing, around the time of her disappearance.

"It's a targeted attack on that data to see if it assists us to find out what happened to Madeleine McCann at that time," Redwood said.

This revelation from the British police is part of a new investigation they set up in July following a two-year review of the case, code-named Operation Grange. Collaborating with Portuguese officials, this investigation is a renewed push to finally provide answers as to how the toddler vanished during a family holiday in a region that's one of the most popular vacation destinations for Brits.

There are currently 41 "persons of interest" in the investigation, police said. However, three of the 15 Brits being monitored are likely to be cleared, according to officials who indicate they will be of no further interest to the investigation.

By examining mobile phone data, authorities said they hope to map out exactly who was in the area at the time of McCann's disappearance and narrow the list of persons of interest considerably. The coastal village, which is situated in Portugal's Algarve region, is home to around 3,000 residents, plus numerous tourists.

Police said this data mining is a refined approach. "This is not a just a general trawl," Redwood said..

While admitting that a "large number" of phones couldn't be linked to specific people, especially those that were bought on a pay-as-you-go basis, Redwood remained optimistic about the operation. When pressed by reporters as to whether phone records held the key to the investigation, he replied, "it could do."

Though Portuguese police did look at phone records during the initial investigation, British police said they weren't examined in detail.

Karen Squibb-Williams of the Forensic Science Society said there is value in returning to these old phone records. "The challenges are considerable, though technology and forensic methodology has significantly advanced over the years and it may be that a technique is available now that was not available at the time," she told ABC News.

The authorities will not be able to access individual text messages but Squibb-Williams noted that by pinpointing locations where calls were made, police may be able to "identify people who were in the relevant areas at key times."

Dr. Tim Stevens, a security expert at King's College London, is less optimistic. While he conceded that technology has improved and that he can't be sure what information the police have, he told ABC News that the latest initiative "smacked a bit of desperation."

Commenting on the timing of the police's mobile data mining, Stevens said, "there's either a specific investigative reason or it's a box that hasn't been ticked."

So far, police said they have waded through 21,614 of the 39,148 documents obtained from the phone traffic. As the rest of the documents are processed, a major appeal will be launched on British television on Oct. 14.