Cpl Wright died in the blast and six others were injured, three seriously
Those responsible for failings that led to the death of a UK soldier trapped in an Afghan minefield should "hang their heads in shame", a coroner has said.
Cpl Mark Wright, 27, of Edinburgh, died and six were injured in four blasts.
Recording a narrative verdict coroner Andrew Walker criticised the MoD and said it was "lamentable" the UK was not equipped to stage an effective rescue.
He said downdraft from a helicopter had set off the fatal mine. The MoD denies troops are lacking proper resources.
Cpl Wright and fellow marooned troops had tried to wave away the RAF Chinook, which was not equipped with the winch they had requested and which they predicted could set off another explosion.
Six of the other soldiers injured lost limbs during the incident on 6 September 2006.
Armed Forces Minister Bob Ainsworth said the government had agreed to pay compensation to Cpl Wright's family and were "determined" to learn lessons from the incident.
The inquest verdict listed a catalogue of failures that would make "very difficult reading" for the Ministry of Defence, said BBC correspondent Alex Bushill.
The parents of Cpl Mark Wright said lessons must now be followed
But Commander of Joint Helicopter Command, Rear Admiral Tony Johnstone-Burt, denied the rescue Chinook had set off the explosion and said he was "confident" current resources enabled British forces to carry out the tasks they faced.
Rear Adm Johnstone-Burt - who is responsible for the provision of all battlefield helicopters and crews in Afghanistan and Iraq - said in addition to UK Chinook, Apache, Sea King and Lynx helicopters, British forces had access to other helicopters provided by allies.
He said all UK helicopters deployed in Immediate Response Team roles in Afghanistan were now fitted with winches, but went on to say they did not expect British forces to use helicopter winches to extract personnel from minefields "because of the lethal risks involved".
He also said: "Our thoughts are with the family and friends of Cpl Mark Wright GC at this difficult time. The heroic actions of Cpl Wright and those injured in this incident were motivated by a selfless desire to save their comrades."
Commander of Joint Helicopter Command, Rear Admiral Tony Johnstone-Burt says the helicopter did not cause the blast
Cpl Wright was posthumously awarded the George Cross for his actions in aiding a colleague and continuing to command the incident despite his own serious injuries.
In a statement from Cpl Wright's family, their solicitor said the coroner had made it clear there had been "really serious systemic failures" in providing the correct training, intelligence and resources for troops to do their jobs.
Mr Walker said that the blast which killed Cpl Wright was caused by the "downwash" from the British Chinook sent to rescue the platoon of Paras who had been stranded in an unmarked minefield.
He said Cpl Wright's death could have been avoided.
"That a brave soldier is lost in battle is always a matter of deep sadness but when that life is lost where it need not have been because of a lack of equipment and assets, those responsible should hang their heads in shame," he added.
The soldiers, who were from the Parachute Regiment's 3rd Battalion, became marooned after one of their snipers strayed into the unmarked danger zone in the Kajaki region of Helmand province.
We are satisfied that Mark did not cause his own death, or contribute to it in any way. This will give us some peace of mind
The troops asked for a helicopter with a winch to be sent to pick up the sniper, whose leg had been blown off.
They were told none was available and the Chinook, which was not fitted with a winch, was sent instead. But when it arrived the concerned soldiers tried to wave it away.
As it departed another mine exploded, striking Cpl Wright.
The survivors were rescued some three hours later by two US Blackhawks which were fitted with winches. Cpl Wright died on board one of the American helicopters.
In delivering his verdict the coroner said three main factors contributed to Cpl Wright's death:
• A lack of availability in Afghanistan of appropriate UK helicopters fitted with a winch. The coroner said there was a lack of suitable lighter helicopters with winches that could have pulled the troops to safety
• The downwash from the Chinook helicopter sent to the minefield
• The administrative delay in sending a suitable helicopter.
The narrative verdict is a statement about how the death occurred, used when the coroner believes their conclusions require detailed explanation.
In his statement Mr Walker also criticised a lack of batteries for radios at observation posts, which hampered the ability to communicate, as well as a failure to provide meaningful information to soldiers about the threat of mines in the area.
He also spoke out against the teaching methods used to train soldiers to locate and mark mines.
Speaking outside the Oxford court as the two-week inquest ended Cpl Wright's father Bobby said he and Cpl Wright's mother Jem were "proud" of the courage their son displayed.
"We are also proud to be associated with the courage of his colleagues, both on that day and in coming to this inquest, to relive those events.
"We are satisfied that Mark did not cause his own death, or contribute to it in any way. This will give us some peace of mind."
He said it had been "painful to listen to the catalogue of errors" that led to their son's death and said they did not want other families to experience the loss of a child in similar circumstances.
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