As the Brexit date under Article 50 of the Lisbon Treaty, which will be 29 March, is looming, May has pledged to present her proposals for the next steps to deal with the Brexit deadlock to parliamentarians on Monday.
The Ministry of Defence said it was supporting no-deal preparations across government to ensure there are "effective and proportionate contingency plans in place".
Earlier, a spokeswoman for May told reporters that a one-page document had been shown to lawmakers during meetings aimed at finding a way forward on Brexit.
After the confidence vote, May met several party leaders, but the main opposition leader, Labour's Jeremy Corbyn, refused to hold talks unless a no-deal Brexit was ruled out.
In ruling out the prospect of No Deal, a future Labour Government would risk losing all leverage.
Political analyst Anand Menon, from the research group U.K.in a Changing Europe, said May had a remarkable ability to soldier on. "The reason a no-deal Brexit is so scary is because tariffs on everything are highly punitive under WTO (World Trade Organization) rules", said Andrew Jackson, head of fixed income at fund manager Hermes Investment Management.
Against the Prime Minister's deal, Remain led by 65% to 35%, while against no-deal was 59%-41% in favour of staying in the EU.
Labour's finance minister-in-waiting, John McDonnell, said May could eventually get a deal through parliament if she negotiated a compromise with his party.
May will therefore tread carefully as she tries to win over opposition lawmakers - many of whom want to remain in the European Union - while also attempting to appease more hardened Brexit-backing coalition partners.
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And no matter what May's negotiating position is now, Blair said that seeking an extension to Article 50 - of delaying Brexit beyond March - was "inevitable".
"No sensible person goes into a negotiation and says I will agree with whatever you want because I have to have any deal".
But the further May moves towards softening Brexit, the more she alienates dedicated Brexiteers in her own party who think the threat of a no-deal Brexit is a crucial bargaining chip.
France's emergency decrees will allow British workers and retirees living in France to continue staying there for a year after March 29 - but only if the British government agrees to do the same for French citizens in the United Kingdom.
The EU and May's government have agreed to what they call temporary arrangements to avoid a "hard" border, at least until the two sides can reach a final agreement.
The most recent polling suggests support for Brexit may be flagging. A small number favour a second referendum.
Once practically unthinkable, a second vote is now talked of as a genuine option.
And fewer than a quarter of those questioned opposed a second referendum on the grounds that it would be a re-run of the 2016 vote. A YouGov survey released Thursday found that when excluding those who said they do not know or would not vote, 56 percent of respondents would choose to remain in the European Union if there was a new referendum, while 44 percent would choose to leave.