Lords voted 335 to 244 for an amendment to give lawmakers the final say on the outcome of Brexit negotiations with Brussels - including staying in the bloc if they do not like the final agreement.
Peers are today set to debate and vote on a series of amendments to try to stamp their demands on Brexit.
Keir Starmer, Labour's Shadow Brexit Secretary, responding to the House of Lords vote to strengthen the terms of Parliament's meaningful vote, said Monday night: "This is a hugely significant moment in the fight to ensure Parliament has a proper role in the Brexit negotiations and that we avoid a no deal situation".
"We will now consider the implications of the House of Lords' decision".
"It is not a mechanism for overturning the referendum". It would give politicians in the Houses of Parliament the power to block the government from walking away from negotiations with no deal.
The Prime Minister has always insisted that MPs and peers would be offered a choice between accepting an exit agreement or allowing Britain to leave the bloc without any deal.
This opens the possibility that they could send ministers back to the negotiating table or even cancel Brexit. It was sponsored by peers across the political spectrum: former Conservative Cabinet minister Douglas Hogg, Labour's Dianne Hayter, William Wallace of the Liberal Democrats, and David Hannay, an independent.
European Union chief Brexit negotiator Michel Barnier gestures as he speaks to members of the media as he arrives to visit InterTradeIreland in the border-town of Newry in the south of Northern Ireland.
Labour's shadow Leader of the Lords, Baroness (Angela) Smith of Basildon said: 'We're half-way through the voting stage but this Bill continues to be an opportunity for the Prime Minister to take a pragmatic view of how best to protect the rights of United Kingdom citizens - rather than be distracted by the ideological pursuits of some of her backbench MPs.
He said: "The truth of the matter is my Lords, a great deal has been spoken about the House of Commons".
"We are disappointed that the House of Lords has voted for this amendment in spite of the assurances we have provided", Minister of state at the Brexit department Martin Callanan said after the vote.
'It asks for meaningless votes on the deal before the deal is done.
It was the government's seventh defeat during the Report stage of the EU (Withdrawal) Bill and several more are forecast.
The British government faced pressure over Brexit at home and overseas Monday, including a defeat in Parliament over who gets the final say on an exit deal with the European Union.
He said the defeats on the legislation preparing for Brexit were a case of the "peers against the people" and that they "have to decide whether they love ermine or the European Union more". 'We are in a position of peers against the people'.