But Ms. May, under pressure from Labour, other lawmakers and global financial markets to offer them more than her catch phrase of "Brexit means Brexit", stopped short of promising a formal vote on her strategy before triggering Article 50 of the E.U.'s Lisbon Treaty.
He has emerged as the key opposition figure on Brexit, even as the Labour Party remains in disarray, and could galvanize pro-Remain lawmakers who want to see a softer Brexit. They worry the government has chose to seek a "hard Brexit", which means leaving the bloc's single market of 500 million consumers in order to exercise more control over immigration.
However, it specifies that any parliamentary scrutiny process must respect the vote to leave the European Union and should not "undermine the negotiating position of the government".
On Tuesday evening, May offered an amendment to accept extra scrutiny as long as it "does not undermine the negotiating position of the government".
Davis dismissed as a "stunt" a move by Labour to pose 170 questions to the government on the detail of the Brexit plan - one for every day until the end of March, the deadline May has set for triggering Article 50.
Appointed prime minister shortly after the June 23 vote on European Union membership, replacing David Cameron who resigned, Ms May has come under pressure to drop her insistence that she will not give a "running commentary" on the Brexit negotiations.
Labour Party Brexit spokesman Keir Starmer accused the government of "sidelining Parliament".
May has ruled out giving Parliament a vote on Article 50, which triggers the exit process, and therefore won't give it a chance to block Brexit.
Fearing that some Tory MPs would rally behind the apparently innocuous Labour motion, May added an amendment to the Labour motion on Tuesday conceding the need for such scrutiny.
"The move this morning was on May's comments but largely because they were initially read as something they weren't: she is not really changing stance, parliament will not be able to veto a hard Brexit", said the head of hedge fund sales at a big currency trading bank in London.
Quick to retaliate, Corbyn said that he was "most grateful to the well over 300,000 people that voted for me to become the leader of my party, which is rather more than voted for her to become leader of her party".
However, it does mean there will have to be a substantive parliamentary debate on No 10's strategy at a later date before the United Kingdom embarks on Brexit.
"Let me give you some examples - first of all the Secretary of State for Exiting the European Union has already made two statements in this House, I believe four hours of questions followed from those".
Senior Tories repeatedly protested over the Prime Minister's apparent support for a "hard Brexit", insisting the June referendum result did not give her authority for a hardline approach to talks over withdrawal from the bloc.