The inquiry's lead attorney has warned that issues with the evidence some government agencies provided to the Covid inquiry could impede its progress.
According to Hugo Keith KC, many departments had responded within "demanding timeframes. ".
He expressed concern, however, about the "insufficient detail" and missed information deadlines in some witness draft statements.
Additionally, he pointed out that some departments, most notably the Cabinet Office, had attempted to redact documents.
The inquiry is currently engaged in a legal dispute with the Cabinet Office over whether or not the inquiry should receive unredacted messages and diary entries from Boris Johnson and other ministers and officials involved in the pandemic.
Some of the messages, according to the Cabinet Office, are "unambiguously irrelevant" to the investigation and may contain information about the personal lives of ministers and other officials.
It should be up to Baroness Hallett, who is in charge of the investigation, to determine what is and is not relevant.
Mr. Keith confirmed that the High Court was likely to hear the case on or shortly after June 30. The government has filed a lawsuit opposing the inquiry's request for unredacted messages.
Mr. Johnson declared last week that he would send the inquiry his unredacted WhatsApp messages instead of going through the Cabinet Office.
The former prime minister's cooperation was acknowledged by Mr. Keith, who added that his team planned to start reviewing the messages later this week.
The team would compare the unredacted and censored messages provided by the Cabinet Office, he said, and hoped to be able to do the same with Mr. Johnson's notebooks and diaries, which are currently held by the Cabinet Office.
Mr. Johnson purchased a new phone as a result of April 2021 security concerns. Therefore, the in question WhatsApps only have messages from May 2021, which is more than a year after the pandemic began.
The inquiry, according to Mr. Keith, had requested that the Cabinet Office "obtain the phone without delay, to confirm in writing the process by which it will be examined, and to give confirmation that it, like the diaries, the notebooks, and the WhatsApps, will be accessed fully.".
The Cabinet Office claimed last week that it had written to Mr. Johnson to warn him that public support for his legal counsel in the Covid inquiry could be withdrawn if he attempted to "undermine" the government.
According to Mr. Keith, he wanted confirmation that the Cabinet Office "was only trying to make sure that Mr. Johnson wasn't going to disclose any material that was protected by national security.".
"From what we understand, the Cabinet Office did not try to stop Mr. Johnson from disclosing information that, in their words, was "unambiguously irrelevant.". ".
The prime minister's spokesman responded that Downing Street was still "hopeful and willing to agree together on the best way forward" when questioned about the lawyer's remarks.
