Her remarks signalled Ms Greening could now join a group of Tory Brexit rebel MPs, who will be watched closely by the Government ahead of the EU Withdrawal Bill's probable return to the House of Commons.
"This Bill is essential for preparing the country for the historic milestone of withdrawing from the European Union", said Mr Davis.
But the unelected upper House of Lords may insist on further changes when the bill moves there for scrutiny later this month, while ministers still face anger from the devolved Scottish and Welsh administrations.
It should allow Britain to continue to function normally as it leaves the EU.
MPs have tabled hundreds of amendments to the bill in recent weeks, many of them focused on its sweeping powers to both change European Union regulations as they are transferred and to authorise any Brexit agreement with the bloc.
Announcing Labour's opposition to the bill at third reading, shadow Brexit secretary Sir Keir Starmer branded it "not fit for purpose" as he repeated demands for MPs to have a meaningful vote on any divorce deal with the EU.
He said: "My committee is strongly of the view that the Withdrawal Bill should be amended so that United Kingdom ministers can only legislate in devolved areas with the consent of devolved governments". With support of 324 MPs, and the opposition of 295 MPs, a government majority of just 29, the bill for Exiting the EU aims to convert all European law into British law.
He said Labour had "repeatedly" pointed out "six serious defects in the Bill", and said: "But we have been talking to a brick wall".
Peers are overwhelmingly pro-European, but they are mindful of their role to scrutinise, not block, legislation.
The Scottish and Welsh Governments previously dubbed the Brexit legislation a "power grab" and have said they can not recommend the devolved legislatures grant it consent in its current form. SNP lawmaker Ian Blackford warned the government it could trigger a "constitutional crisis" with its plans, which have also drawn anger from Wales.
"From the beginning our approach has been to work constructively with MPs from across the House wherever possible to improve the bill". After reaching a deal on the key separation issues in December, Britain is due to start talks with the European Union this month on a transition deal before moving on to the future relationship.
Some 48 Labour MPs, including former Labour Cabinet ministers and ex-members of his own frontbench, backed a bid to keep Britain in the single market and customs union after Brexit.
May has ruled out a second vote and says Britain will be leaving.
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