The upper chamber passed an amendment which asks for MPs to be given a “meaningful vote” on any final EU deal.
However, cross bench peer Lord King, who was the governor of the Bank of England up until 2013, argued the wishes of the British people must be respected.
Mervyn King warned the Lords against meddling with the Brexit Bill
The House of Lords needs to be pretty careful about this
“The House of Lords needs to be pretty careful about this,” he told Bloomberg on Tuesday.
“There was a referendum, the decision was made very clear by both sides that it would be for the people to decide in the referendum.
“That decision has been reached and now it’s the role of Parliament to implement that.”
The former Bank of England chief was speaking on Bloomberg on Tuesday
Opponents of Theresa May want to be able to reject any deal done and ask the Prime Minister to go back and get a better one.
In another blow to the Government, peers voted 366 for and 268 against the clause in its final reading.
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Last week, peers also voted in favour of guaranteeing the rights of EU nationals.
However, Lord King argued the current legislation was only for beginning the process of leaving the bloc.
He continued: “There is no doubt that over the next two years or so there’ll be a lot of discussions and there will be some set of arrangements brought before the House of Commons for a vote.
“It would be quite wrong for the House of Lords at this stage to try to lay down conditions as to what should be the process which is followed at the end of that period.”
All the pictures from Brexit Bill Tuesday Tue, March 7, 2017
Theresa May is facing a second defeat on her Brexit bill Tuesday as the House of Lords votes on another change which would give parliament the final say on leaving the EU
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Archbishop of Canterbury, Justin Welby, speaks in the House of Lords Chamber at the start of the third day of The European Union (Notification of Withdrawal) Bill
During June’s historic referendum campaign, Remainers warned of grave consequences for Britain’s economy if the country opted for Brexit.
Lord King rebuked the claims, insisting “very little had changed” since the vote to Leave.
He added: “I think we’ve learned a great deal about the political excitement that Brexit has induced.
“I think one of the most striking contrasts is that Brexit has little impact on the economy and may, in the long run, have little impact.”