The government climbdown, just hours after Downing Street said that it would not compromise further on the meaningful vote proposals, underlines the fragility of the prime minister's grip on her party and her lack of room for manoeuvre on Brexit.
But if the amendments being debated in Parliament this week force a change to the government's negotiating strategy, the wound could yet reopen.
Rebels had been pushing for an amendment that would have given Parliament unprecedented powers over the final stages of Brexit talks.
The shock move came as the Prime Minister warned senior ministers in her Cabinet that defeat on a series of Lords amendments over the next two days would undermine the Government and make negotiations with Brussels harder.
The opposition Labour Party wants to force the government to negotiate a Brexit deal where the United Kingdom retains "full access" to the EU's single market and that would ensure "no new impediments" to trade.More news: Trump says USA to stop war games with S. Korea
If agreed, ministers would have until the end of November this year to secure a Brexit deal before seeking the approval of parliament.
Phillip Lee accused the government of trying to limit parliament's role in shaping Britain's departure from the European Union and said the government's Brexit strategy was detrimental to the British people.
The result followed a day of high drama as a justice minister in May's government resigned in order to back the amendment.
Opening the debate in parliament, the Brexit secretary, David Davis, had said the government could not accept anything that could undermine May, hinting that the amendments proposed by Lords and Tory rebels would hamper negotiations.
Tory chief whip, Julian Smith, scurried up and down the green benches of the Commons, speaking urgently to groups of MPs including Grieve.More news: Central Pa. law firm representing Triple Crown-winning horse
"We all hang together or we will hang separately", Buckland added, in a plea for unity.
Brexit campaigners still expressed concern that the concession may open the door to the European Union trying to force Britain into retaining the closest possible ties with the bloc by weakening the government's hand in the talks.
Earlier, most of the original 11 rebels on the meaningful vote amendment had indicated that they would stand firm. Labour will only vote for a final Brexit deal if it delivers a strong relationship with the Single Market based on full tariff-free access and ensures no loss of rights and standards. Rebels have said they will challenge May's plans to leave the customs union during votes on other bills, on trade and customs, which will be brought back to the house some time before July 24.
In Tuesday's key vote, the government headed off a potential Conservative backbench rebellion and the vote passed by 324 votes to 298.More news: Tech stocks gain as USA confirms ZTE deal
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