The lawyers are seeking an urgent injunction to stop the UK government and police "inspecting, copying or sharing" data seized from him during David Miranda's detention.
Miranda, the Brazilian partner of Glenn Greenwald, was stopped on Sunday in connection with classified data leaked to the 'Guardian' newspaper.
The UK Home Office has told the court that "tens of thousands of highly classified documents" had been seized when 28-year-old Miranda was detained under Schedule 7 of the Terrorism Act 2000 on his way from Berlin to Rio de Janeiro.
He also wanted police to reveal with whom they may have shared information taken from his client.
Ryder told Lord Justice Beatson and Justice Kenneth Parker that Miranda was questioned and property in his possession was seized "under threat of criminal prosecution in a coercive use of Schedule 7 which was unlawful".
Gwendolen Morgan, of Bindman Partners, argued in a witness statement in court that the decision to use schedule 7 "amounted to a grave and manifestly disproportionate interference" with Miranda's human rights and was incompatible with the European Convention on Human Rights.
UK home secretary Theresa May has defended the police's use of anti-terrorism laws to hold and question Miranda.
She said such action "was right" if police thought Miranda was holding information useful to terrorists.
The incident has sparked international outrage as Greenwald has been reporting extensively on American and British surveillance programmes for the 'Guardian', based on leaks from US whistleblower Edward Snowden.
The former contractor with the National Security Agency in America has been granted temporary asylum in Russia.
