The probe will assess whether dozens of killings were illegally carried out and investigate the alleged cover-up by the Royal Military Police.
It will begin substantive hearings at the Royal Courts of Justice on Monday into the claims between 2010 and 2013, with submissions on behalf of the families of 33 people, including eight children, who were allegedly killed by special forces in Afghanistan.
The probe was launched in the wake of legal challenges to the government by Leigh Day solicitors on behalf of the Saifullah and Noorzai families, as well as a number of significant media investigations.
One member of the Saifullah family said since a raid by British forces, they are “having nightmares and dreams filled with difficulties”.
Ahead of counsel's opening submissions to the inquiry, they said: “On February 16, 2011, as a consequence of a night raid on our house by the British forces, my father, Haji Abdul Khaliq, my two brothers, Sadam Hussein and Atta Ullah, and my cousin, Ahmad Shah, were killed.
“Before their killings, our family had a very beautiful life. This was a very difficult, saddening and painful night.
“Since this raid by the British forces on our house, we have lost our normal sleep and are having nightmares and dreams filled with difficulties.
“When this incident took place, we lost everything.
“My family and I request the inquiry team to provide us with the truth and explain to us why and on what basis we had to go through this cruelty.”
Mansour Aziz has called on the inquiry to listen to two children who were allegedly severely injured during a night raid on his family home on August 6, 2012.
“In 2012, our house was raided by foreigners and my brother and sister-in-law were killed and their two children severely injured while they were sleeping in their bed,” he said.
“We want to know the truth and why it was our house that was raided.
“We are asking for the court to listen to these children and bring justice.”
Two RMP investigations, code-named Operation Northmoor and Operation Cestro, are set to be scrutinised by the inquiry.
No charges were brought under Operation Northmoor – a £10 million investigation which was set up in 2014 to examine allegations of executions by special forces, including those of children.
Operation Cestro saw three soldiers referred to the Service Prosecuting Authority, but none were prosecuted.
Leigh Day partner Tessa Gregory said the families involved in the investigation hope it will “fearlessly uncover the truth of the death of their loved ones”.
“Our clients hope that the opening of this inquiry marks the end of 'the wall of silence' and obstruction that has confronted them over the last decade,” she said.
“The bereaved families look to the inquiry to fearlessly uncover the truth of the deaths of their loved ones and to ensure that those responsible are held to account.
“Proper accountability must involve those at a senior level in the armed forces and in government who are responsible for the management and oversight of our most elite forces.”
The independent statutory inquiry was commissioned by then-defence secretary Ben Wallace under the 2005 Inquiries Act.
A Ministry of Defence spokesman said: “The MoD is fully committed to supporting the inquiry as it continues its work.
“It is not appropriate for us to comment on allegations which may be within the scope of the statutory inquiry and it is up to the statutory inquiry team, led by Lord Justice Haddon-Cave, to determine which allegations are investigated.”