Mr Howlin said he fears "endless fudge until we run out of time" in relation to the border between Northern Ireland and the Republic.
The parts of his amendment which he expects to be taken forward by ministers provide a mechanism by which Parliament has to be consulted by the end of November in the event of no deal or if a proposed agreement is rejected, he said.
However, despite backing down, pro-Remain Tories signalled they would not be easily consoled by a compromise offered by ministers.
The Government has managed to fend off a major rebellion after parliament rejected an amendment to bring a "meaningful vote" on the final Brexit deal.
"In all conscience, I can not support the Government's decision to oppose this amendment because doing so breaches such fundamental principles of human rights and Parliamentary sovereignty".
"It will be down to the Government to come back to Parliament not just with a statement that we can do nothing about, but with something that we can vote on to say whether we're happy or not".
In his resignation letter, he said he wouldn't be able to "look my children in the eye" if he supported Brexit in its "irresponsible" current form.
MPs were told that one parliamentarian had to be accompanied to a public meeting by a six armed police officers because of threats over their stance on Brexit.
It is thought that both the government and the Remainer group of Tory MPs consider the outcome to be a success.
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Soubry reminded the House of Commons of the 48% who were being ignored by the government. "We have no doubt of what was going on".
"The Brexit secretary has set out three tests that any new amendment has to meet - not undermining the negotiations, not changing the constitutional role of Parliament and government in negotiating global treaties, and respecting the referendum result".
Asked whether such concessions would nowAsked whether such concessions would hamper Britain's negotiating hand, Mr Grieve continued: "I disagree with that entirely".
The amendment would effectively give MPs the power to prevent the United Kingdom from opting to crash out of the European Union without a Brexit deal and is a major victory for Remain-supporting MPs in parliament.
Shadow Brexit Secretary Keir Starmer commented: "This vote was about ensuring parliament was given a proper role in the Brexit negotiations and that we avoid a no deal situation, which is becoming more likely with the divisions at the heart of this government".
Leading Conservative rebels welcomed the "important concessions" by the government, but insisted that ministers must follow through on their concession or face a defeat when the bill returns to the House of Commons later this month.
"However, facing the prospect of a humiliating defeat, Theresa May has been forced to enter negotiations with her backbenchers and offer a so-called concession".
The UK published its "backstop" plans last week, after a reported tussle over the wording between Mr Davis and Prime Minister Theresa May.
"We will put in front of Parliament the decision for them to vote. after that there will be a process of primary legislation to put the actual details of it in Parliament, so Parliament will actually decide on the application of the detail".