from The Guardian's announcement article, 'Guardian Partners with NYT over Snowden GCHQ files':

Journalists in America are protected by the first amendment which guarantees free speech and in practice prevents the state seeking pre-publication injunctions or "prior restraint".

It is intended that the collaboration with the New York Times will allow the Guardian to continue exposing mass surveillance by putting the Snowden documents on GCHQ beyond government reach. Snowden is aware of the arrangement.

Freedom of Information
A British newspaper wants to take its aggressive investigations global, but money is running out.
By Ken Auletta, The New Yorker, available online now and in October 7, 2013 issue

[....] Since June 5th, the Guardian had been publishing top-secret digital files provided by Edward Snowden, a former contract employee of the National Security Agency [....]

Such articles have become a trademark of the Guardian. [....]

Now Rusbridger was poised to publish a story about how the G.C.H.Q. not only collected vast quantities of e-mails, Facebook posts, phone calls, and Internet histories but shared these with the N.S.A. [....]

Heywood had learned about the most recent revelation when Guardian reporters called British authorities for comment; he warned Rusbridger that the Guardian was in possession of stolen government documents. “We want them back,” he said. Unlike the U.S., Britain has no First Amendment to guard the press against government censorship. Rusbridger worried that the government would get a court injunction to block the Guardian from publishing not only the G.C.H.Q. story but also future national-security stories. [....]

At 5:23 P.M., roughly eight hours after the encounter in his office, Rusbridger ordered the Guardian to post the G.C.H.Q. story on its Web site and then in its print edition. Although the British government had taken no further action, the mood in the Guardian’s offices was anxious. As the stories based on Snowden’s revelations were taking shape, Rusbridger had hired additional security for the building and established a secure office two floors above the newsroom, just down the corridor from the advertising department, to house the documents. When he flew to New York to work with his team there on the stories, “he couldn’t talk on the phone,” his wife, Lindsay Mackie, said. “He couldn’t say what was going on.” [....]

Extensive story on The Guardian's situation--goes on for 9 pages.