The officer in charge of a renewed Metropolitan police investigation into the disappearance of Madeleine McCann says he hopes to solve the case, five years after she disappeared from a resort in Portugal.

Detective chief inspector Andy Redwood told BBC's Panorama programme that he and his 35-strong team will begin analysing nearly 40,000 documents in what he says is the best opportunity for finding the child, who disappeared on 3 May 2007, just before her fourth birthday.

Redwood, who is leading Operation Grange, which was set up after an intervention from David Cameron last year, said his team had access to all of the available evidence on the case gathered by Portuguese police and private investigators.

He said that this wealth of information offered the "best opportunity" to find leads, which would then be presented to police in Portugal who continue to lead on the investigation.

"There is, ultimately, a process of us turning every single piece of paper over and interpreting and analysing what is contained within them," he said.

So far, the new review of the McCann case has cost taxpayers £2m.

The former home secretary Alan Johnson, who was also interviewed for the programme, which airs tonight, called on Cameron to launch a "charm offensive" on the Portuguese government to help boost the McCanns' profile and get further co-operation from the country's police. "A bit of diplomacy can ensure that you do get the co-operation you need," he said.