With just six months to go, there is no full exit agreement and some Conservative MPs have threatened to vote down a deal if she manages to get one.
Khan said Britain now faces either a bad deal or a no-deal Brexit, both of which are "incredibly risky" for Britain.
May said that if she got a deal, she thought parliament would ultimately approve it.
Despite strong opposition in her Conservative party and criticism in Brussels, May has stuck by the so-called Chequers proposal to keep close trade ties with the European Union after Brexit on March 29 next year.
Speaking to BBC's Andrew Marr earlier today, he said: "Let me tell you the facts, which are that the police now are preparing for the possibility of civil unrest".
British Prime Minister Theresa May has warned that her Brexit plan is the only alternative to crashing out of the European Union without agreement, in an interview broadcast Monday.
British finance minister Philip Hammond, speaking alongside Ms Lagarde, said the government had to heed the "clear warnings" from the International Monetary Fund of a no-deal Brexit.
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The IMF said that even a good deal would mean new barriers to trade. The economy will grow around 1.5 percent this year.
"It's ensuring that we get that good deal from the European Union which is good for people in the United Kingdom, wherever they live in the United Kingdom, that's what's important for us".
Supporters of Brexit, who admit there may be some short term instability, say British ministers and business chiefs are spreading scare stories about the impact of a "no-deal" in an attempt to rally support behind May's plans.
Former foreign minister Boris Johnson, who quit in July in protest at the Chequers plan, launched a fresh attack on it in his weekly newspaper column on Monday. "It is still a hard border", the prime minister said.
"The whole thing is a constitutional abomination, and if Chequers were adopted it would mean that for the first time since 1066 our leaders were deliberately acquiescing in foreign rule", Johnson said, referring to the 11th Century invasion which established Norman rule over England. "The ancestors of many people we represent fought alongside the British in two world wars, but are now forced to stand aside in favour of people with no connection to the United Kingdom".
European Union officials and diplomats insist that nothing has fundamentally changed on the so called backstop plan for the Irish border.
He said it will be up to the House of Commons in the future to "chart this nation's destiny" and decide what to do if Brussels law changes.
No new border plan will materialise before the Conservative Party conference on September 30-Oct 3, the diplomat said.