Britain has been plunged into crisis as a result of the second rejection of Mrs May's deal, which MPs voted against 391 votes to 242, The Times says.
"In the light of our own legal analysis and others, we do not recommend accepting the government's motion today".
"She is simply saying it reduces the chances of us being kept in the backstop", Wilson told LBC radio, in reference to the so-called "Irish backstop" - the policy within the Withdrawal Agreement aimed at making sure no hard border appears between Northern Ireland and Ireland.
Mrs May said: "The deal we've negotiation is the best and only deal available".
"If we leave without a deal, we will set the majority of our import tariffs to zero, whilst maintaining tariffs for the most sensitive industries", Trade Policy Minister George Hollingbery said in a statement.
With EU leaders warning there would be no more changes or negotiations, and less than three weeks to go until the U.K.is due to leave, British lawmakers were facing a stark choice in a vote later: support a deal many consider inadequate or run the risk that Brexit might happen chaotically, or not at all.
Sinn Féin President Mary Lou McDonald meanwhile said: "The British Parliament voted by a landslide to reject the Withdrawal Agreement and Theresa May's latest proposals".More news: Verizon launches 5G in Chicago, Minneapolis at $10 extra cost
However, lawmakers are expected to vote against a no-deal Brexit and then, on Thursday, vote in favour of seeking a delay to Brexit.
However, this concession from the European Union failed to impress the British parliament as the new type of backstop had no clear end date and it cannot be ended unilaterally by the parties.
On the Irish border, the British government said it would not introduce any new checks or controls on goods moving from the Irish Republic to the British province of Northern Ireland in the event of a no-deal Brexit, stressing the plan was temporary and unilateral.
Many business leaders have spoken about the potentially disastrous consequences of a no-deal Brexit.
Carolyn Fairbairn, director-general of the Confederation of British Industry, said the no-deal arrangements would be "a sledgehammer for our economy".
Mr Lidington told MPs in a late night sitting in the Commons that the PM had secured legally binding changes that "strengthened and improved" the withdrawal agreement.
"Finally, the House of Commons is going to have to make a final judgment on what it wants in terms of Brexit", he said.More news: Drug Charge Results in Halted Sales of ‘Yakuza’ Spin-Off Game ‘Judgment’
Just 18 days before the United Kingdom is due to leave the European Union on March 29, there is still no ratified divorce deal and talks with the bloc have stalled as May tries to break the political deadlock in London.
May is offering the possibility of a "short, limited" delay, but is herself opposed, warning that eventually MPs will have to make a decision about Britain's future.
A rejected deal and postponement of the March 29 Brexit date will leave Britain "in uncharted waters", the paper added.
May lost her first meaningful vote on the deal on 15 January in a historic defeat by 230 votes.
The spokesman for Northern Ireland's pro-Brexit Democratic Unionist Party, Sammy Wilson, said the party rejected the legal assurances that UK Prime Minister Theresa May negotiated with European Commissioner Jean-Claude Juncker in Brussels on Tuesday.
Brexiteers in May's party accuse her of surrendering to the European Union and it was not clear if the assurances she agreed would be enough to win over the 116 additional lawmakers she needs turn around the crushing defeat her deal suffered on January 15.More news: 10 things you need to know about Safety Jabrill Peppers