The government faces further parliamentary hurdles as its Illegal Migration Bill returns to the Commons on Tuesday.
New amendments have been announced to quell safeguarding concerns for detained children and pregnant women.
But MPs will vote on changes backed by the House of Lords after the draft legislation suffered 20 defeats in the upper chamber.
It comes as MPs heard the Home Office is paying for thousands of empty hotel beds reserved for migrants to avoid overcrowding at processing centres.
The Home Office offered a series of concessions on Monday evening, including limits on the detention of unaccompanied children, who will be granted immigration bail after eight days rather than the current proposed 28.
Another change will prevent people who have already entered the UK without permission from being removed retrospectively after the legislation receives royal assent.
The government will also keep the current limit of 72 hours on the detention of pregnant women – though this can be extended to seven days on the authorisation of a minister.
It comes after the Bill was mauled in the Lords, where peers demanded a series of revisions including modern slavery protections and asylum help for unaccompanied children.
The defeats raised the prospect of a prolonged stand-off between peers and the government during so-called parliamentary ping-pong, when legislation is batted between the Lords and Commons.
The government is expected to seek to overturn many of the amendments, but said on Monday it has accepted some changes in an attempt to ease the Bill’s passage through Parliament.
The government still faces potential challenges despite the changes, with Theresa May and Iain Duncan Smith among senior Conservatives to air concerns that the legislation must go further in offering modern slavery protections.
Home Office second permanent secretary Simon Ridley told the Commons Public Accounts Committee the Government department keeps a “buffer” of about 5,000 beds across the country in case of a sudden influx of Channel crossings in a bid to avoid more problems with overcrowding at the Manston processing centre in Kent.
He later added: “We have got excess beds that we are paying for that we can move people into immediately,” to which MPs expressed surprise at the number set aside.
The Bill is central to Rishi Sunak’s pledge to “stop the boats” – one of five key commitments for his leadership – which remains mired in difficulties.
It aims to ensure those who arrive in the UK without government permission will be detained and promptly removed, either to their home country or a third country, such as Rwanda.
But critics have argued it is morally unacceptable and unworkable, and the Rwanda plan is now set for a battle at the Supreme Court.
Mr Sunak has said he is “throwing everything” at the pledge and insisted the government remains confident that the plan is the “fair”, while Home Secretary Suella Braverman said Monday’s amendments would “help this crucial legislation pass through Parliament swiftly”.