In the run-up to the general election, the Chilcot Inquiry into the Iraq war is being kept out of the public eye, with no new documents published during the campaign in order to keep out of party politics. But the result of the election could well impact on the inquiry. Liberal Democrat and Conservative parties have both promised to rethink the way it operates if they are in government after Thursday’s poll.

The Liberal Democrats have said they would introduce a fast-track freedom of information procedure and ensure the publication of key documents that the inquiry has been prevented from publishing. The Tories have repeated a threat to “revisit” the terms of the inquiry.

Since Gordon Brown announced the inquiry last June, he has come under fire from opposition parties for its lack of transparency. The prime minister initially said the inquiry that would sit in secret, but had to backtrack after fierce criticism from MPs on all sides and former mandarins, including former cabinet secretary Lord Butler, who led a 2004 inquiry into the use of intelligence in the run up to war.

In November, as public hearings began, Liberal Democrat leader Nick Clegg ambushed Brown in the Commons after it became clear that a Cabinet Office protocol would severely limit the inquiry’s ability to publish and publicly discuss the documents that, according to chairman Sir John Chilcot, form the “great bulk” of its evidence.

Chilcot and other committee members have since expressed their frustration during hearings at the restrictions. In January, Tories and Liberal Democrats called for the “gag” on the inquiry to be lifted after former attorney general Lord Goldsmith said while giving evidence that he did not agree with the government’s decision to prevent publication of key papers.

The inquiry has not published any new documents since early February. I asked its spokesman whether this was because none had been cleared by the government or because the inquiry had chosen not to publish any during the run-up to the election. He referred me to Chilcot’s closing statement [pdf] on 8 March that “The Iraq Inquiry intends to remain out of the public eye over the period of the election.” The implication of this is that if the inquiry has documents that it is entitled to publish it has chosen to deny voters knowledge of their contents.

But a new Liberal Democrat or Tory government or coalition could see significant changes to the way the inquiry operates. Liberal Democrat shadow foreign secretary Ed Davey told me: “Labour has suffocated the Iraq Inquiry with rules and red-tape, effectively preventing publication of key documents. Liberal Democrats will review the protocol and appoint an arbitrator between the Cabinet Office and the Iraq Inquiry to rule on the publication of documents. This will act as a fast-track freedom of information procedure and ensure transparent and swift publication of documents.”

A Conservative spokesman said: “We have always said that a Conservative government will reserve the right to revisit the terms of the Inquiry. At the same time we have accepted that the Inquiry needs to hold some of its sessions and proceedings in confidence.”

The Labour party did not take up my invitation to comment but neither Labour nor ministers have given any indication that they plan to loosen the existing restrictions on the inquiry.