They ask that "no inspection, copying, disclosure, transfer, distribution or interference" of Miranda's data contained in the seized devices is performed before the legality of the seizure has been determined, and if any of that has already happened, that no "product of that inspection" is "disclosed, shared or used further in any way."
They also demand to be informed whether "any other public authority or third party - either domestic or foreign - has been granted possession or access to that data (or copies of it)", so that they could request those same things of them.
Finally, they requested that all the seized electronic equipment is returned to Miranda within 7 days of them being taken, for the authorities to agree that the detention, questioning and seizure of their client's confidential journalistic and other material was unlawful, to agree to return all property and destroy all copies of materials retained, and to confirm that they have not been shared with any third parties.
In the meantime, Home Secretary Theresa May has stated publicly that she was informed in advance of Miranda's possible detention at Heathrow Airport. "If it is believed that somebody has in their possession highly sensitive stolen information which could help terrorists, which could lead to a loss of lives, then it is right that the police act and that is what the law enables them to do," she commented.
As regards the destroying of the documents The Guardian received from Edward Snowden, it has been revealed that the UK government demanded it because foreign cyber forces or terrorists might hack into the publication's IT network and retrieve them, and that it threatened to stop The Guardian from reporting on the leaks via legal action if they don't comply with the request.
Even though Guardian's editor Alan Rusbridger stated that that couldn't happen as the documents were not stored on the publication's network, the agents tasked with retrieving or destroying the documents were unmoved, and Rusbridger finally decided he would rather have the documents destroyed that hand them over to the authorities.
It has also been disclosed that UK Prime Minister David Cameron authorized the destruction of the disks and files.