Detectives investigating the disappearance of Madeleine McCann are looking for a lone intruder who sexually abused five girls during break-ins at holiday homes.
The tanned, dark-haired man is suspected of breaking into 12 properties where British families were staying in the Algarve, Portugal between 2004 and 2010.
In four of the incidents, girls aged between seven and ten were sexually assaulted.
These attacks happened between 2004 and 2006, before Madeleine vanished in 2007.
Madeleine was nearly four when she disappeared from her family's holiday apartment in Praia da Luz in the Algarve on 3 May 2007 as her parents dined at a nearby restaurant with friends.
Detective Chief Inspector Andy Redwood said tracing the man, said to have "an unhealthy interest in young, white female children", is one of his priority lines of inquiry.
His team currently have 38 people classed as "persons of interest" to the inquiry.
They are also sifting through details of 530 known sex offenders whose whereabouts they cannot account for.
Of those 59 are classed as high priority, and some of those are British.
British investigators have so far sent three international letters of request to Portuguese authorities over the investigation, covering 41 priority areas for the team.
Deputy Assistant Commissioner Martin Hewitt said he is frustrated at how slow the legal process has been.
"That's causing us frustration because we know what we want to do and we are ready to go with that but the process is the process," he said.
Another 30 letters have been written to other European countries, but the force would not reveal where.
British detectives launched a fresh investigation into the disappearance in July last year.
Two years into a review of the case they made renewed appeals on television in Britain, the Netherlands and Germany.
Portuguese authorities said last October that a review had uncovered enough new information to justify reopening the inquiry, after it was shelved in 2008.