Ten years after the disappearance of their daughter, Kate and Gerry McCann still buy her Christmas and birthday gifts.

It’s one of many signifiers that as May 3 – the anniversary of the day four-year-old Madeleine vanished – approaches, the couple have not given up hope of finding their eldest child.

Twice they thought she had been found, and twice they felt the pang of disappointment when sightings of the toddler turned out to be red herrings.

Both false alarms occurred within a year of Madeleine going missing while on a family holiday in Praia da Luz, Portugal.

Former BBC reporter Clarence Mitchell, who has worked with the family as their media spokesman, recalled the incidents in an exclusive piece for the Telegraph.

"Twice in the 10 years I have worked with the McCanns, I genuinely thought we were within reach of finding their missing daughter, Madeleine," Mitchell wrote.

The first happened just a few months Madeleine's disappearance when an anonymous caller claimed the little girl was hidden at a farm in in Seville near the border of Spain.

"I started to get phone calls, always at three o’clock in the morning, always the same ghostly man’s voice, repeatedly naming a farm where she was being hidden."

Unfortunately, when the property was raided the child was nowhere to be found.

"As it was raided, and turned out to look exactly as he had painted it in those calls, I really felt we were on to something. But she wasn’t there, and those tip-offs - like so many others that we received from hoaxers, ransom seekers, conmen and psychics - were never explained."

The second false alarm came at the end of 2007, when the McCanns had moved back home to their with their two-year-old twins, Sean and Amelie.

"Spanish private investigators working on their behalf had found a blonde-haired girl who spoke English in a village in the Atlas Mountains of Morocco. All the information coming back to us suggested heavily that it could be Madeleine, so much so that an aircraft was put on stand-by, with its engines running, waiting to fly to pick her up.

"Kate and Gerry sat tight. They had learned by that stage to be skeptical, not to give in to natural hope only for it to be dashed. They preferred to wait until the Moroccan authorities had checked it out. And when they did, it became clear she was not Madeleine."

These days the McCanns rarely appear in the media, but with the 10-year milestone quickly approaching they sat down with The Mirror's Fiona Bruce.

Listen: Loren O'Keeffe shares an insight into what it's like when a loved one goes missing. (Post continues after podcast.)

They told the journalist they are still hunting for their daughter.

"I think it's been good for the general public to hear police say there's no evidence that she's dead, and that there is still an active investigation, and there is still hope. So certainly from my point of view, somebody knows what's happened," Gerry said.

Kate added: "It might not be as quick as we want, but there's real progress being made and I think we need to take heart from that and we just have to go with the process and follow it through, whatever it takes for as long as it takes. But that there is still hope that we can find Madeleine."