Labour is attempting to force the government to publish all internal documents relating to the Windrush scandal to find out who was to blame.
The party says it will use the same parliamentary procedure that led to the release of Brexit impact studies.
Amber Rudd resigned as home secretary after a series of leaked documents showed she had been told about immigration removals targets.
Labour says it now wants to hold Prime Minister Theresa May to account.
Shadow home secretary Diane Abbott said: “With the resignation of Amber Rudd, Theresa May has lost her human shield and must now fully account for the policies she created and drove through from the Home Office into Downing Street.
“The Windrush scandal has exposed something rotten at the heart of government. We need to know what has led to this situation.
“If the prime minister is too weak to be accountable, Labour will have to force her to be accountable. We have had enough of ministers trying to dodge questions and blame others, we need full disclosure of all the facts.”
Last year, Labour used what it called an “ancient but still effective” parliamentary procedure to force the government to release 58 documents assessing the impact of Brexit on different industrial sectors.
This involved tabling a motion that “an humble address be presented to Her Majesty” requiring that the reports “be laid before this House” and given to the Brexit select committee.
In January, after a three-month battle, the government released a redacted version of the reports to the Brexit committee. MPs were allowed to view the documents in a secure reading room.
In March, the select committee decided to publish all but one of the documents, which was deemed to be too sensitive.
On Wednesday, Labour plans to table a similar motion in a vote on an opposition day debate on the Windrush scandal.
It will call on the government to provide the Home Affairs Select Committee with all papers, correspondence and advice – including emails and text messages – from 11 May 2010 up to 1 May 2018, between ministers, senior officials and special advisers relating to policy decisions with regard to “Windrush generation” cases.
New Home Secretary Sajid Javid has promised to “do right” by the people affected by the Windrush scandal and to stop using the using the phrase “hostile environment” to describe tough immigration laws introduced by Mrs May when she was home secretary.
But Labour says the government is covering up details of deportations and re-entry refusals, as well as warnings about the impact deportation targets had on people’s lives.
Ms Rudd admitted she had “inadvertently misled” the home affairs committee when she told it: “We don’t have targets for removals.”
In her resignation statement, she said: “I have reviewed the advice I was given on this issue and become aware of information provided to my office which makes mention of targets. I should have been aware of this, and I take full responsibility for the fact that I was not.”
In a separate development, Immigration Minister Caroline Nokes has given a personal apology to those affected by the Windrush scandal.
Speaking at a meeting of the All Party Parliamentary Group on Race, she said it was important for her to be there “to say sorry.”
The minister spoke to Paulette Wilson, a grandmother who was detained and threatened with deportation as a result of not being able to prove her status, who was at the meeting.
Ms Nokes said the government had a “huge job to do to gain trust” and added that she hoped “it will not take too much time”.