MPs are set to vote on whether the Government should guarantee that European Union nationals can stay in Britain after it pulls out of the bloc.
Labour will hold a debate and force a division in the Commons in an effort to ramp up pressure on Theresa May, the frontrunner to succeed David Cameron as prime minister.
The Home Secretary has so far failed to guarantee the status of three million EU nationals living in the UK, insisting it must be a part of Brexit negotiations despite a furious backlash from Tory MPs.
Brexit campaigners such as former Ukip leader Nigel Farage, who has pledged to work "informally or formally" with the next prime minister on those negotiations, have condemned Mrs May's stance.
Mr Farage said he was "disgusted" while Labour MP Gisela Stuart, who chaired Vote Leave during the referendum campaign, criticised her for using EU nationals as "bargaining chips".
Labour made clear it expected Mrs May to respond to shadow home secretary Andy Burnham at the beginning of the debate and called on candidates for the Tory leadership to declare their position in the vote.
The Opposition day debate and vote is non-binding and will have no effect on Government policy although if Labour's motion is backed by a significant number of Tory MPs it will put pressure on ministers.
Ahead of the debate, Mr Burnham said: "It is simply not good enough for the Home Secretary to say that she 'hopes' EU nationals will be allowed to stay.
"These are people who have put down roots here, with children, families, caring responsibilities, who pay taxes and contribute to our economy and society.
"They deserve much better than being used by the Government as bargaining chips.
"Having opened up the question, it is essential that the Home Secretary puts her leadership campaign on hold and comes to the House."
The debate comes as Britain's historic vote to leave the EU continues to fuel concerns there will be an economic slowdown.
On Tuesday, Bank of England governor Mark Carney unveiled a move to boost lending by up to £150 billion under plans to contain the fallout as the pound plunged to fresh 31-year lows.
His announcement came as two investment firms suspended trading in their property funds with investors scrambling to pull their money out of UK commercial property holdings.
Aviva moved to halt trading in its £1.8 billion property fund, while asset manager M&G Investments temporarily suspended trading in its property portfolio and feeder fund.
Their decision came a day after Standard Life Investments stopped dealing in its £2.7 billion UK Real Estate fund.
The suspensions hit the pound, which dropped below 1.31 US dollars for the first time since 1985 and sunk to its weakest level against the euro since 2013 at 1.17 euro.