David Davis has been accused of treating Parliament with contempt and attempting to reduce its sovereignty after withholding information about the economic impact of Brexit from MPs.
Prominent Conservatives are among those expressing anger after the Brexit secretary refused to hand over full expert assessments as to the likely impact of leaving the EU on 58 sector of the British economy.
The Government was ordered to release the dossiers to the Brexit Select Committee following a House of Commons motion.
But instead it redacted key details, on the basis that the information was too sensitive and could potentially undermine the Brexit negotiations in Brussels if it was leaked outside the Committee by MPs.
Mr Davis has been summoned urgently to appear before the Brexit Select Committee to explain his actions.
Its chairman Hilary Benn also warned the Committee will need to consider whether his actions are in breach of Parliamentary privilege.
"I do object to any suggestion that the select committee or I as chair cannot be trusted to do our job," he said.
There was also anger and outrage at the Government's stance in the main Commons hall.
Shadow Brexit secretary Sir Keir Starmer was among those answers from Mr Davis - but the Brexit department sent junior minister Robin Walker to respond instead.
As Mr Walker responded in the Commons, there were cries of "Where is he?" from Labour MPs angry at Mr Davis's absence.
Commons Speaker John Bercow said the urgent question was not the time to debate whether a contempt of the House had occurred, adding "there may or may not be later occasions for that matter to be discussed".
Sir Keir responded: "Whether he is in contempt of Parliament is a matter we will come to at a later date, but he is certainly treating Parliament with contempt."
Former Cabinet minister Ken Clarke accused the Government of reducing parliamentary sovereignty to a "ridiculous level" during the debate.
"If the Government wished to resist the publication of the papers it had it should have voted against the motion, and if it wished to qualify or to edit the papers that it had it should have sought to amend the motion," he said.
"We cannot allow post-Brexit to start reducing Parliamentary sovereignty to a slightly ridiculous level."
Prominent Tory Brexiteer Jacob Rees-Mogg also said the Government's stance was unacceptable as he urged them to release all the documents.
"To meet this motion it is not at the discretion of the Government to decide what to take out. It is now at the discretion of the select committee," he said.
"I therefore urge the Government either to meet the terms of the motion in full or to seek to put down a new motion."
Ministers have insisted the information does not exist as 58 separate impact assessments as requested by Parliament, but was instead "a wide mix of qualitative and qualitative analysis" compiled since the referendum.
Mr Walker added that all the information could not be passed to the committee because it "did not give any firm assurances that what was passed to them would not subsequently be published in full".
Downing Street has backed the approach taken by Mr Davis.
The Prime Minister's official spokesman said: "We believe that we have complied with the terms of the motion.
"We have collated around 800 pages of documents which we believe meets the request."