Key documents relating to the police detention of David Miranda, the partner of the Guardian journalist Glenn Greenwald, have been handed over to his lawyers, the high court was told on Wednesday.

Judges turned down an application for more material to be released on the grounds that further disclosure was not necessary and would not be in the national interest. The decision was announced at the end of a preliminary hearing before next week's challenge of the lawfulness of the police decision to hold Miranda under schedule 7 of the Terrorism Act 2000.

The Brazilian national was detained for nine hours as he passed through Heathrow airport on 18 August this year. He was in transit between Berlin, where he had met the film-maker Laura Poitras who has been involved breaking revelations based on documents leaked by Edward Snowden, and Rio de Janeiro.

Miranda's lawyers claim that the Metropolitan police misused schedule 7 and that his detention was a violation of his human rights. They sought information about why Miranda was stopped and why his laptop, phone and electronic equipment were seized.

Matthew Ryder QC, representing Miranda, told the court: "We are concerned we have not had adequate disclosure. We have achieved some significant disclosure. There are some significant documents that are not with us." Passages in many of the released documents were heavily redacted, he said.

Stephen Kovats QC, counsel for the home secretary, Theresa May, told the court that officers did not know before they stopped Miranda what material he was carrying. "The base line against which the risk to national security is assessed is the entirety of the material misappropriated by Mr Snowden," Kovats said.

Declining to order that any more material should be released, Lord Justice Laws ruled that "any further disclosure is unnecessary to do justice to the case. The public interest against disclosure asserted by the [home secretary] is obvious and compelling … Everything that ought to be disclosed has been disclosed."

The judge read from a section of the internal port circulation sheet (PCS), which formally set out the reasons for Miranda's detention. It said that "intelligence indicates that Miranda is likely to be involved" in espionage activity that had the potential to "act against the interests of UK national security". Disclosure of the material he was carrying, it said, fell within the definition of terrorism.

The PCS document said the grounds for making a stop also covered "the disclosure or threat of disclosure [where it] is designed to influence a government and is made for the purpose of promoting a political or ideological cause".

The full hearing is due to take place next week. Laws said it was the court's expectation that the police officers involved in the decision to stop Miranda would be present, although they may not be called for cross-examination.

The three judges in the administrative court turned down a request by Greenwald to join the case as a co-complainant.

Gwendolen Morgan, Miranda's solicitor, said outside court: "We are pleased that material has been handed over at the last minute and that Lord Justice Laws accepted that there is an important issue for the courts to deal with. He also accepted that Miranda's rights to freedom of expression are engaged by the case."

Greenwald is to leave the Guardian shortly to join a media organisation being created by Pierre Omidyar, the founder of eBay.