May said the government would not instruct her own party's lawmakers how to vote, as would normally be the case.
Andrea Leadsom, who manages government business in parliament, insisted however that "it is still our intention, if at all possible, to leave the European Union on March 29 with a good deal".
British lawmakers, who on January 15 voted 432-202 against May's deal, are studying the assurances and Cox's legal advice before the vote later on Tuesday.
On Wednesday, lawmakers are expected to reject a no-deal Brexit in a vote at 1900 GMT and on Thursday are then due to vote on whether to ask the European Union for a delay to Brexit, something to which all the bloc's other 27 members must agree.
Some British lawmakers had warned their Brexit-backing colleagues that rejecting the deal could lead to Britain's departure being postponed indefinitely, because a delay would give momentum to opponents of withdrawal.
And Education Minister Nadhim Zahawi said it would be "consistent for all of us in Government to leave no-deal on".
The UK has vowed to have no checks at the Irish land border for goods crossing into Northern Ireland in the event of "no deal" departure from the European Union.
"Our "no-deal" preparations are now more important than ever before".
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"The belated, cack-handed way in which the government has handled its no-deal planning is one of the main reasons why many businesses will not be prepared for this outcome by 29 March", Renison said.
"This regime is only temporary as we recognise that there are challenges associated with this approach, including the unmonitored flow of goods into the United Kingdom and the potential for exploitation of any new system", the government said in a statement".
Backbench MPs and opposition parties have put forward six amendments to show which direction they want the government to take on Brexit.
The decision - created to avoid the need for checkpoints which might revive sectarian tensions - has raised fears of smuggling, as ministers insist there will not be a border down the Irish Sea. "Now is the time to come together, to back this improved Brexit deal, and to deliver on the instruction of the British people".
The stakes could hardly higher - and the future looks uncertain - after May failed for a second time to get Parliament to sign off on a divorce deal that was the culmination of two years of tortured negotiations.
But tariffs will be slashed on imports from outside the EU, potentially lowering prices on goods from countries like the U.S. and China, in a move which unions warned would "destroy" jobs in manufacturing sectors like steel.
May's fellow Conservative parliamentarian Bob Seely underscored Mrs. In the staunchly pro-Brexit port of Dover in southern England, retiree Mary Simpson said she felt that her voice as a "leave" voter had not been heard. May's warning in a tweet, saying: "Today is our Hotel California moment".
Sterling, which had earlier in the day fallen by 2 percent to $1.3005, was trading at around $1.3086 shortly after the vote. Ms May said the House of Commons will debate the improved deal on Wednesday. However, GBP bulls could take comfort from the increasing prospect of Parliament wresting control from the Government, with a snap general election and a second referendum both still possible, albeit unlikely for now.