The US today said it would allow the release of footage to a coroner's inquiry that shows a US air attack on a British military convoy in Iraq.

The Pentagon had previously refused permission for the tape to be shown at the inquest into the death of Lance Corporal Matty Hull, despite the demands of British coroner Andrew Walker to the Ministry of Defence.

Its U-turn follows the leaking of the footage today. A transcript of the cockpit video records the US pilot and another on the same mission swearing and possibly weeping after they realise they have attacked friendly forces.

"I'm going to be sick," one says on being told that the attack has killed a coalition soldier. He adds: "We're in jail, dude."

The two US A-10 jet pilots were both believed to be reservists with no previous combat experience at the time of the attack on March 28 2003. The Sun, who obtained the video, identified them as POPOV36, a lieutenant colonel, and POPOV35, a major.

The defence secretary, Des Browne, welcomed the decision to allow the coroner and the Hull family to view the video. "The release of classified information, even for the closest of allies, is never straightforward, but this is the right thing to do," he said. "I recognise that this must have been distressing for the Hull family, and I'm glad that we have been able to resolve it."

Earlier today, the coroner's office said the Sun had promised to give Mr Walker a copy of the tape and would use it in court if the newspaper did so. "This material is now in the public domain, and that means that it can be used in the Matty Hull inquest," a spokesman said.

Lance Corporal Hull died in a burning armoured vehicle three days before his 26th birthday after the US planes opened fire on a Household Cavalry Regiment patrol near Basra, southern Iraq. Four other British soldiers were injured.

The MoD refused to comment on the contents of the tape, which appears to show that one of the primary mistakes was made by US ground controllers, who assured the pilots there were no "friendly" patrols in the area.

The Sun said the two pilots were on a mission to destroy Iraqi artillery and rocket launchers north of Basra, and were circling at an altitude of 3,500 metres (11,480ft) when they saw Iraqi vehicles and a British patrol.

As the pair looked at the British convoy, POPOV36 twice said he thought he could see orange panels on the vehicles - an indication of coalition forces.

But after a ground controller assured the pilots they were "well clear of friendlies", POPOV36 decided the orange panels were most likely to be rocket launchers and opened fire, with his colleague saying: "Get him, get him."

POPOV36 apparently saw wounded soldiers being dragged from the burning vehicles, and said: "It looks like he is hauling arse. Ha ha."

The pilots were then told by ground controllers that there were, in fact, "friendly" light tanks in the area, prompting a volley of swearing.

They asked another ground controller about the fate of the convoy, and were told one person was dead and another had been injured.

"I'm going to be sick," POPOV35 said, while his colleague swore again and made a crying sound.

"Did you hear?" asked POPOV35, getting the reply: "Yeah, this sucks". POPOV35 then said: "We're in jail, dude."

Lance Corporal Hull's family have said they were initially told no such tape existed.

It first came to light when Mr Walker said he had been handed a copy and wanted to play it before the hearing.

On Friday, after an initial deadline for the MoD to get permission to use the tape had passed, Mr Walker adjourned the inquest until March 12 and gave the ministry a week to confirm it would allow the tape to be played.

MoD officials said they had not been able to get permission from US authorities to release the classified tape.

The constitutional affairs minister, Harriet Harman, who called last week for US authorities to help the inquest in any way they could, today pointedly refused to condemn the leaking of the tape.

Asked whether it was right to leak the recording, she said: "I have always taken the view that what is important is that the families get all the information available to help them understand what happened."

Ms Harman has held a series of meetings with the US embassy's deputy chief of mission, David Johnson, to urge that the tape be approved for use at the inquest.

Asked earlier today why Washington had so far refused this, Mr Johnson said US soldiers were sent into combat under "a set of predictable laws which are established before the fact".

"One thing I want to make very clear is our heart goes out to this family," he told Radio 4's Today programme.

"This is an extraordinary tragedy that they have endured and we are very sorry for what has happened.

"But I think that does not take away from the need to have a body of law which is followed and a set of expectations we can have our combat forces - yours and ours - go by when they go into battle."