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.
A Ministry of Defence spokeswoman said: "Our thoughts remain with the family and friends of Private Cheryl James.
"This decision is a matter for the Attorney General and the courts. "If a new inquest is ordered, we will of course provide support to the coroner when needed."
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.
The Government's chief legal adviser has given permission to the family of a young Army recruit who died at Deepcut barracks to apply for a fresh inquest into her death.
Attorney General Dominic Grieve QC has granted Private Cheryl James' family consent to apply to the High Court for a new inquest into her death, nearly a decade after it happened.
Pte James, 18, was undergoing initial training at Deepcut Barracks when she was found with gunshot wounds in November 1995.
She was one of four young soldiers who died at the barracks in Surrey between 1995 and 2002, sparking allegations of bullying and abuse.
Lawyers representing families of dead Iraqis admitted there was "insufficient evidence" to back their claims British soldiers unlawfully killed civilians nearly a decade ago.
From the outset the families have had the simple objective of discovering the extent of any wrongdoing and, if so, how it came about and who was responsible.
It is accepted that, on the material which has been disclosed to date, there is insufficient evidence to support a finding of unlawful killing in Camp Abu Naji.
The Iraqi core participants will not submit that, on the balance of probabilities, live Iraqis captured in the course of the battle died or were killed at Camp Abu Naji.
However, PIL said there were still allegations of mistreatment of prisoners for the inquiry to consider.
The Al-Sweady Inquiry is examining allegations British troops mistreated and killed 20 or more Iraqi detainees after the Battle of Danny Boy in May 2004. The MoD has vigorously denied the claims, saying any deaths occurred on the battlefield.
Claims that British troops unlawfully killed Iraqis a decade ago have been dropped by the families of the deceased who admitted there was "insufficient evidence."
On the last full day of evidence at the year-long Al-Sweady Inquiry, Public Interest Lawyers, who are representing the families of the deceased, said there had been "insufficient evidence" to back their allegations that civilians were killed while in British troops' custody in May 2004.
PIL said it came to the decision after the end of military evidence and "the current state of disclosure by the Ministry of Defence".
The inquiry has heard evidence from hundreds of witnesses both here and abroad, at a cost of more than £22 million.
Allegations British soldiers unlawfully killed Iraqi civilians a decade ago are not supported by evidence heard by a public inquiry investigating their deaths, a lawyer acting for the families of the dead told the Al-Sweady Inquiry in London today.
The inquiry has been examining claims that UK soldiers murdered 20 or more Iraqis, and tortured detainees after the "Battle of Danny Boy" in Maysan Province, southern Iraq, in May 2004.
Defence Secretary Philip Hammond has accused a committee of MPs of failing to recognise the need to counter evolving threats, such as potential cyber-attacks, meant there had to be a shift in the balance of defence spending.
Mr Hammond said:
It is not possible to maintain traditional regular forces at historic levels while also investing in countering the threats of tomorrow.
The Army 2020 structure is not simply about a reduction in size; it is a complete overhaul of how the Army works to deliver a fully-integrated force, using a better mix of regulars, reserves and contractors to get the maximum defence effect from the budget.
An influential group of MPs has warned that if ministers attempt to make any further cuts, the whole Army 2020 plan would "unravel" completely.
Under the plan, the size of the regular Army is being slashed from 102,000 troops to 82,000 while the numbers of part time reservists will expand to 30,000 by 2018.
In a hard-hitting report, the Commons Defence Committee said the rationale for the plan remained untested while the "high level of change" involved - at a time when troops were still engaged in Afghanistan - could "compromise" its ability to respond to emergencies.
It complained at the "apparent lack of consultation and involvement" of the head of the Army, General Sir Peter Wall, who was simply told by the senior civil servant at the Ministry of Defence what the future strength of the Army would be.
Government cuts to the Army have not been thought through and could leave Britain dangerously exposed in the event of a future crisis, MPs have warned.
The Commons Defence Committee said the restructuring progamme - known as the Army 2020 plan - was driven by the need to fit a "financial envelope" rather than a proper assessment of potential threats.
It has urged the Ministry of Defence to draw up contingency plans for a rapid recruitment programme in case there was urgent need for more troops to deal with an emergency.