With MPs having more of a say in the process, it is possible they could push for a "plan B", which would see Britain adopt a softer Brexit, such as staying in the EU's satellite trading bloc the European Economic Area - the so-called Norway option.
News of the delay caused the pound to tumble to its lowest level in 18 months.
One participant in the march told NHK that the prime minister won't listen to the people who chose to leave the EU.
"But, also I have to say I think it is going to be very hard for Theresa May to persuade anybody that she will be able to do this better the next time".
After speaking with EU leaders including EU President Donald Tusk and German Chancellor Angela Merkel at the weekend, she said she would continue talks ahead of a Brussels summit on Thursday and Friday. "The vote is going ahead", a spokesman said.
Brexit supporters and May's nominal allies in Northern Ireland's Democratic Unionist Party say it could leave Britain forced to accept European Union regulations indefinitely, or Northern Ireland treated differently from the rest of the United Kingdom.
Cleveland Cavaliers get Matthew Dellavedova in three-team trade with Bucks, Wizards
Cleveland got guard Matthew Dellavedova , centre John Henson and future first- and second-round picks, all from Milwaukee. He averaged 6.3 points and 3.7 rebounds but missed significant time with a severely sprained left ankle.
"They also agreed that preparations for a "no deal" outcome should intensify", it said.
Before the vote was delayed, analysts had been focusing on the number of votes May could win or lose by and what that could mean for her chances of renegotiating a deal.
European Union leaders will attempt to help Theresa May sell the Brexit deal to sceptical MPs this week after the prime minister's chaotic climbdown over the "meaningful vote".
Theresa May has been fighting to rally support for her Brexit agreement which MPs were expected to vote for on Tuesday evening.
Britain's Prime Minister Theresa May tours the Royal Welsh Winter Fair at the Royal Welsh Showground in Builth Wells, Wales, Britain.
Earlier today, the Prime Minister's spokeswoman described the conference call with ministers due at 11.30am as routine. "One worry that I have is, some people of course want us to re-open the withdrawal agreement".
Kate Middleton nails Christmas style in thousand-dollar plaid
Louis was born in April as he joined the growing Cambridges family including brother Prince George and sister Princess Charlotte .
Gove, the environment secretary and a key Brexit voice in the cabinet, told colleagues that while May could seek new concessions from Brussels, there was a risk of her - or another leader - returning with a worse deal.
"The government has lost control of events and is in complete disarray", said opposition leader Jeremy Corbyn.
Britain is scheduled to leave the European Union on March 29, 2019.
The European Court of Justice ruled Monday that when an EU member country has notified its intent to leave, "that member state is free to revoke unilaterally that notification".
Some EU officials have however mentioned the possibility of changes to the accompanying political declaration on future trade ties between Britain and the EU after Brexit.
"We are replacing the business with a new statement but it isn't a motion and therefore isn't votable", the source said.
Thousands of Northern Ireland O2 customers lose data services over technical issue
An additional seven million customers of Sky, Tesco, Giffgaff, and Lycamobile, which O2 provides services for, are also impacted. O2 issued the following statement on its website: "Our technical teams are investigating reports of issues when using data".
MPs successfully called for a 3-hour emergency debate on the situation Tuesday.