By a vote of 245 to 218, the unelected upper chamber, the House of Lords, supported an amendment to her Brexit blueprint, the EU withdrawal bill, requiring ministers to negotiate continued membership of the European Economic Area, meaning that it would remain in the single market. London says it has already presented a position paper and wants to get on with working out a deal.
And Ukip's deputy leader, Mike Hookem MEP, branded the House of Lords "an archaic and anti-democratic hangover from a bygone age".
There are now 13 key issues the Commons will have to decide whether to reverse thanks to the House of Lords.
"It is time to make Britain truly democratic and replace the House of Lords with an elected upper chamber with fixed terms of office".
Not every Labour peer was behind the legislation change, as former minister Andrew Adonis described the amendment as "useless".
May has insisted Britain quitting both the European single market and customs union when its membership of the EU ends.
Tory peer Lord Callanan added: "I do not believe that anything would be gained from its acceptance in the Bill apart from confusion and uncertainty".
They voted 311 to 233 in favour of a cross-party amendment arguing that 29 March, 2019 should not be on the face of the legislation as it risked tying the hands of the UK's negotiators.
But Boris Johnson yesterday called on the upper house to respect the "clearly mandated" will of the people.
French Minister Warns Air France Will "Disappear" Unless Crisis Stops
France's economy minister on Sunday warned that the survival of Air France was now in the balance. However, the French government assured that it will not be responsible for the company's losses.
Newby, who was one of four peers who tabled the amendment, said: "It was frankly ridiculous to enshrine this date in law from the get-go".
"It is not just the referendum but in the general election too".
'There is a longstanding tradition in the United Kingdom that the House of Lords can under no circumstances frustrate what has been clearly mandated not just by a referendum but by the election as well.
"Indeed, they shouldn't frustrate it under any circumstances because they do not represent they sovereign will of the British people".
The Guardian newspaper commented that the 13th defeat for the government has suffered was probably the one that does most to challenge the government's Brexit plans because it is created to keep Britain in the European single market.
"Of course that is a critical national interest and we will have to deal with that accordingly".
This prompted Brexit minister Lord Callanan to actually agree with the remain-supporting peer for once, saying: "The amendment may have been tabled with one eye on the withdrawal agreement, but ministerial colleagues and I have been very clear throughout this Bill's passage, both within this House and in the other place, that this Bill's aim is just to create a functioning statute book as we depart from the European Union".
The aim was to revert to the original wording of the Bill, he said.