The government has suffered a heavy defeat on a crucial Lords vote that could pave the way for parliament to send ministers back to the Brussels negotiations if MPs vote down Theresa May’s Brexit deal.

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Labour said the amendment, which is the seventh Lords defeat for the government on the EU withdrawal bill, would effectively prevent Britain crashing out of the EU with no deal. The cross-party amendment was supported by 19 Tory rebels, winning by a majority of 91.

Ministers have previously warned that should parliament vote down the deal agreed by negotiators, Britain would leave the bloc with no agreement. The amendment, led by former Tory minister Douglas Hogg, would change that scenario, meaning parliament could alter it and ask the government to reopen EU talks.

The measure is designed to enhance Conservative MP Dominic Grieve’s amendment to the EU withdrawal bill, guaranteeing MPs a vote on the final deal, which won a shock victory in the Commons in December.

Keir Starmer, the shadow Brexit secretary, called the vote “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”.

The leader of the Liberal Democrats in the Lords, Dick Newby, said the amendment “puts parliament in the driving seat”.

Rebel Tory sources have said they hope to attract cross-party support in the Commons for the plan, giving remainers the confidence to vote against a damaging Brexit deal without the fear that it will trigger a “no deal” outcome where the consequences would be worse.

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During the debate, Hogg told peers the clause was “designed to ensure that the future of our country is determined by parliament and not by ministers”.

He said a choice between accepting the terms or crashing out of the EU would not be a genuine choice. “This is not regaining control. To act in such a manner would be to impose ministerial decisions on parliament by coercion,” he said, calling it “an elective dictatorship of a particularly flagrant kind”.

Echoing Margaret Thatcher, under whom he said he was “privileged to serve”, Hogg said his response was: “No, no no!”

He called the referendum vote “at the very best an interim decision” and said the public could not have predicted the terms of the UK’s departure.

Lib Dem peer Lord Roberts said he was deeply concerned about the sweeping powers of the government, likening it to the 1933 Enabling Act conferring absolute power on Adolf Hitler. “Perhaps I’m seeing threats that do not exist, but they are there, they are possible,” he said.

However, the former Tory leader Michael Howard made a scathing speech about the amendment, saying it could precipitate a constitutional crisis. He said: “[The House of Commons] is not a negotiating body; it has never taken that role, I don’t believe it wants that role and I don’t believe it should have that role ... it would immeasurably weaken the government’s negotiating position with the EU and would I believe make our government and our country a laughing stock.”

Later in the debate, the Brexit-backing Green party peer Jenny Jones said she had come to the House of Lords prepared to vote for the amendment on the basis of parliamentary sovereignty, but said she had been put off by the speeches of pro-remain peers.

“Quite honestly, the speeches in favour have turned me against them,” she said. “There is clearly more of an agenda than control of the process.”

Speaking after the vote, Lord Callanan, a minister in the Department for Exiting the European Union, said the amendment would “weaken the UK’s hand in our negotiations with the EU by giving parliament unprecedented powers to instruct the government to do anything with regard to the negotiations – including trying to keep the UK in the EU indefinitely”.

The government also lost a vote on a cross-party amendment led by Labour peer John Monks, which would give parliament even greater powers over the Brexit negotiations, though Lords sources played down the significance of the victory. Peers voted to back the amendment by 270 to 233.

The amendment calls on ministers to seek parliamentary approval for their phase two negotiating mandate – similar to the process that exists at the EU level, where leaders of the EU27 approve the mandate of Michel Barnier’s negotiating team.

Brexiters have said it fundamentally undermines the government. Writing for the Sun, the Brexit secretary, David Davis, said: “Firstly, the amendment tries to secure a vote for parliament before the negotiations have concluded. This is, quite frankly, nonsensical – because nothing in this negotiation is agreed until everything is agreed.

“Second, it demands specific votes by artificial deadlines which, if not met, would give parliament the power to micromanage the government on how to carry out these negotiations.”

Davis said the change would give the EU commission “a clear incentive to delay the negotiations or present unacceptable propositions”.