Unelected peers backed the amendment to allow Britain’s continued participation in EU agencies by 298 votes to 227, a majority of 71.
The highly controversial move, pushed through by ardent Remainers, will also ensure future EU laws can be replicated on the UK statute book.
The vote is the 11th time the House of Lords has defeated the Government over Brexit since it started debating the EU Withdrawal Bill.
The Government’s latest defeat has further stoked fears that out-of-touch peers are trying to frustrate the will of British voters for a clean Brexit.
The House of Lords have gone well beyond their remit
Ukip MEP David Coburn reacted to the news with fury, telling Express.co.uk: “By meddling in Brexit, the House of Lords have gone well beyond their remit.
“It’s time they all stepped aside. The whole upper chamber is full of cronies of Tony Blair and David Cameron.
“They represent the London bubble, and they’re going against what Brexit voters want.
“Why should they be picking up a fat cheque for trying to rewrite the Brexit legislation? That’s absolutely wrong and unacceptable.”
The House of Lords voted for the UK to remain part of EU agencies after leaving the bloc
And Ukip’s deputy leader, Mike Hookem MEP, branded the House of Lords “an archaic and anti-democratic hangover from a bygone age”.
He said: “The House of Lords is becoming its own worst enemy in trying to reverse the will of the electorate and keep the UK in the EU by any means possible.
“Peers have no faith in the British people to govern ourselves and prosper without the interference of the EU in every aspect of our daily lives.
“Not one of these people, who sit in sneering judgment of the 17.4 million people who voted for Brexit, has been elected to hold such power over our democratic process.
“It is time to make Britain truly democratic and replace the House of Lords with an elected upper chamber with fixed terms of office.”
Arch-Remainer Lord Adonis branded the amendment ‘useless’
Even Labour peer and arch-Remainer Lord Adonis branded the amendment “useless” and said it had “zero impact”.
He told the Lords: “We should concentrate on things that are of real substance, the customs union, the single market, the referendum, these are real changes.”
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.”
But Labour’s Brexit spokeswoman Baroness Hayter urged peers to vote for the amendment.
She said: “Every mention in this House and beyond of those EU agencies have included a plea for us to remain members, associates or partners.”
Labour’s Brexit spokeswoman Baroness Hayter urged peers to vote for the amendment
Earlier today, Foreign Secretary Boris Johnson urged the upper house to respect the “clearly mandated” will of the British people.
He said: “Both parties campaigned to come out of the single market and customs union.
“It is not just the referendum but in the general election too.
“There is a longstanding tradition in the UK 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 vote is the 11th time the House of Lords has defeated the Government over Brexit
Last week, Brexit Secretary David Davis warned that amendments passed by Remainer peers could risk undermining negotiations with the EU.
Mr Davis told MPs that the Brexit Bill was “an essential bill in the national interest” because it ensures Britain will leave the 28-member bloc.
However, he added: “Some of the proposals put by the House of Lords could have the effect of undermining the negotiation.
“Of course that is a critical national interest and we will have to deal with that accordingly.”
After the Lords, the EU Withdrawal Bill will return to the House of Commons.
Both houses have to agree on the final wording of the bill before it can become law.