The statement added: “A team of forensic specialists along with mountain rescue personnel were dispatched to the site in order to catalogue the scene and recover Esther.
“At this stage an accident is the most likely hypothesis, given the location and other early indications. A full investigation is under way to confirm the details surrounding this tragedy.
“The family remain incredibly grateful for the efforts of the police units involved and their commitment to understanding the exact circumstances of Esther’s death.”
Ms Dingley, 37, had been walking solo in the mountains near the Spanish and French border and was last seen on November 22.
A mountain runner raised the alarm on July 23 after discovering what he believed could be the remains of a body at a mountain pass called Port de la Glere.
The Spanish Civil Guard informed their French counterparts after confirming it was on their side of the border.
The remains were subsequently confirmed as Esther’s following DNA tests.
Police teams had been continuing to comb the mountains in the area to try to find the rest of her body and belongings, including a tent and rucksack.