Britons will not need visas for short stays in the EU even if there is no Brexit deal, the European Commission has said.
However, time is running out to meet the deadline for a November EU summit.
The EU Commission said that if no deal was reached, this arrangement would start from 30 March, and if a deal was agreed, it would begin from the end of any transition period, which is now scheduled to be at the end of 2020.
Last month, more than 500,000 people marched in London to protest against Brexit.
There are whispers in Westminster and Brussels this evening that a deal could be on, with the main stumbling-block to an agreement - the Northern Ireland "backstop" now largely agreed by European Union negotiators, according to reports.
Even with such measures in place, the British government says leaving the European Union without a deal could cause major economic disruption, with gridlock at ports and disruption to supplies of foods, goods and medicines.
"If what we've heard is true, this fails to meet the Conservative Party's manifesto, and it fails to meet numerous commitments the prime minister makes", Conservative Jacob Rees-Mogg, one of the hard-line leaders of the Brexit campaign, told the BBC.
DUP deputy leader Nigel Dodds noted that he would not make a judgment on the tentative deal until he sees formal details, but as he told local media Tuesday, "if the reports are as we are hearing, then we couldn't possibly vote for that". Downing Street believes that significant progress has been made over the past 48 hours towards meeting that deadline.
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The leaders of the four main opposition parties, including Corbyn and The Liberal Democrats' Vince Cable, have jointly written to May demanding a "truly meaningful vote" on the deal.
The failure to agree with the European Union means that there is an increasingly hard time period before British Parliament could make a "meaningful final vote" on May's deal before the European Union summit scheduled for December 13-14.
Former foreign secretary Boris Johnson, a leading Brexit supporter who quit the government in July over May's approach, said he would fight the draft agreement.
"We do not want to punish the United Kingdom", he said, adding: "We have to respect the vote in the United Kingdom". "We've done all we can".
In a sign that some are running out of patience with United Kingdom infighting, German Europe minister Michael Roth said the time for a deal "overripe".
The UK government confirmed reports that May's most senior ministers would read the details of the draft agreement on Tuesday evening before a special Cabinet meeting at 2 p.m. on Wednesday.
It is not thought that any deal will be on the table at the Cabinet meeting in 10 Downing Street on Tuesday, which will instead hear an update on negotiations and discuss preparations for a possible no-deal withdrawal from the EU.
The experience from previous such crunch points in this process is that, despite threats to the contrary, it is likely that the majority of ministers will ultimately wave the deal through, give or take a couple of potential resignations.