Earlier in the day, the Lords had riled Brexiteers by backing an amendment aimed at giving Parliament power to set the Government's future course on Brexit if it ends up rejecting any deal agreed by Theresa May later this year.
The peers from the Upper House voted 335 to 244 in favour of an amendment to the EU (Withdrawal) Bill that could allow Parliament to send Britain back to the negotiating table with Brussels or even halt the country's exit from the EU if it is not happy with the final offer.
Peers have voted to give Parliament a potentially decisive say over the outcome of Brexit talks.
They also supported a move to give Parliament approval of the mandate for negotiations over the UK's future relationship with the European Union and backed a post-Brexit system that enables lone child refugees to join family members living in the UK.
Leaked government reports show that every possible deal to leave the European Union will leave the British people significantly worse off than remaining in the European Union, which will have a major impact on frontline services like the NHS, and a number of MPs from across the aisle have called on the government to safeguard these services in negotiations.
"She said it was vital to ensure the legislation is able to deliver the smooth Brexit which is in the interests of everybody in the United Kingdom".
SNP MP Stephen Gethins MP said the defeat was the "most damaging" the government had suffered.
He said: "If Parliament votes down the Article 50 deal, then Parliament must decide what happens next".
"In democracies both Parliament and the electorate have the right to change their minds".
Supporters of the move argue that MPs should have the power to send Mrs May back to the negotiating table if they disapprove of her deal - or if she can not reach one.
Lord Hailsham, who introduced the amendment, told peers ahead of the vote that the Brexit referendum was "at best" an "interim decision" and the people's decision should be "tested" in a second vote.
The bill will soon go back to the House of Commons where MPs will debate the amendments added to it by their colleagues in the House of Lords.
The amendment is opposed by the government and can be overturned in parliament's lower chamber, where May has a slim majority. "This is a massive defeat for the Government".