Not-for-profit organisations have called for "maximum transparency" after eight Cabinet ministers were granted core participant status for the Leveson Inquiry into media standards.

The ministers, including Prime Minister David Cameron, Deputy Prime Minister Nick Clegg and Culture Secretary Jeremy Hunt, have been given the right to see documents and witness statements in advance.

Four groups, Full Fact, English PEN, the Media Standards Trust and Index on Censorship, are asking Lord Justice Leveson to publish the names of any senior civil servants who will see the confidential material and are also asking that it is not made available to special advisers.

The groups, each of which has been a witness at the inquiry, also want details about any government requests to redact any information.

In an urgent application to the inquiry, they said: "All our concerns stem from an interest (and the public interest) in the transparency of the inquiry process, and consequent public faith in the inquiry and its outcomes.

Core participant status, given to people who have a significant interest in the hearings or may face criticism, was also granted last week to Business Secretary Vince Cable, Education Secretary Michael Gove, Justice Secretary Kenneth Clarke, Home Secretary Theresa May and Chancellor George Osborne.

The groups argue that the decision, made on Friday, could pave the way for "anyone whom a minister might entrust to assist him or her to be put forward to join the confidentiality circle".

Referring to the resignation of Hunt's special adviser Adam Smith, who admitted he went "too far" in contacts with News Corp lobbyist Frederic Michel, they added: "The role of Special Advisers has already been at issue in this process, with the resignation of the special adviser to the Secretary of State for Culture, Olympics, Media and Sport. Whereas ordinary civil servants are subject to a general requirement to behave with impartiality and objectivity, Special Advisers are expressly exempt."

They said that "maximum transparency is in the interest of all core participants", adding "we can imagine no good reason why the Government would object to any of the directions we are seeking".