The Government has suffered its first defeat of the new Parliament.
It was swiftly followed by two more losses as the House of Lords amended the Withdrawal Agreement Bill.
Despite having a majority of 80 MPs in the House of Commons, the government lacks a majority in the Lords.
Peers reversed a provision in the Withdrawal Amendment Bill, passed by the Commons.
The Lords changes would mean EU citizens would have the right to physical proof of their right to remain in the UK.
The can reverse this change when the Bill returns to the Commons in a few weeks.
Minister Brandon Lewis tweeted: "I disagree with the results of today’s @UKHouseofLords vote.
"The EU Settlement Scheme grants #EUcitizens with a secure, digital status which can’t be lost, stolen or tampered with.
"There will be no change to our digital approach."
Later, the Government crashed to a second defeat on ministerial powers over the courts to depart from European Court of Justice judgments. Voting was 241 to 205, majority 36, for a cross-party amendment to delete the power from the Bill, amid warnings of it being an interference in the independence of the judiciary.
A third defeat for ministers swiftly followed the second as peers backed a move to allow cases to be referred to the Supreme Court to decide whether to depart from EU case law.
Tory sources vowed to reverse the changes.
Baroness Dianne Hayter, Shadow Brexit Minister said: “None of what is being proposed in these cross-party amendments will stop Brexit happening later this month.
"Indeed, they would strengthen the role of Parliament, preserve the distinction between the power of the Courts and the Executive, acknowledge the Sewel Convention and safeguard the wellbeing of both EU citizens and child refugees.
“The government would do well to heed concerns from across the House of Lords, rather than cock a tin ear towards the amendments.”
