The parents of the soldier who was found dead from a single gunshot wound at Deepcut barracks in November 1995 said they were "delighted" to have a fresh inquest into her death.
But Mr and Mrs James said "a meaningful inquiry into Cheryl's death is almost 20 years late."
When young people die in violent circumstances, a rigorous and transparent investigation should be automatic.
Something went dreadfully wrong at Deepcut yet until now no-one has bothered to look at how and why our daughter died.
We can only hope that Cheryl's legacy helps change the current ineffective and discredited military justice system.
The High Court has ordered a fresh inquest into the death of soldier Private Cheryl James who died at Deepcut barracks after a challenge by her family.
Mr Justice Mitting and Judge Peter Thornton QC both agreed that there was "an insufficiency of inquiry" at the 1995 inquest and quashed its open verdict.
Pte James, 18, was found dead from a single gunshot wound in November 1995.
Judge Thornton said "the discovery of new facts or evidence" made "a fresh investigation including a fresh inquest necessary or desirable in the interests of justice".
Pte James was one of four soldiers who died at the Surrey barracks between 1995 and 2002 amid claims of bullying and abuse.
Privates Sean Benton, James Collinson and Geoff Gray also died from gunshot wounds.
The family of Cheryl James say they are relieved at the Attorney General's decision to allow them permission to apply for a fresh inquest into the death of their daughter.
Pte James was one of four soldiers who died at Deepcut barracks in Surrey between 1995 and 2002.
We're relieved and delighted by the Attorney General's decision.
It's truly an emotional day - it's been a long and painful process, with so many hurdles, but we never considered giving up.
Cheryl had her whole life in front of her; when our young people lose their lives serving their country, not only do they deserve a full and independent investigation into their deaths, it must be their absolute right.
We may now finally achieve a meaningful inquiry into her death and we hope it brings about real change for future recruits.
Private James' parents, backed by Human Rights campaign group Liberty, called for a fresh inquest into her death, lodging an application with the Attorney General for consent to apply to the High Court for one.
Today a spokesman for Dominic Grieve said he had granted his consent.
The spokesman said:
The application was made to the Attorney General on the basis that the original inquest made insufficient enquiry into the circumstances of her death and because new evidence is now available that was not put before the inquest in December 1995.
The Attorney General granted his consent because he concluded that it was in the interests of justice for the application for a new inquest to go forward and to be heard by the High Court.