To avoid an abrupt no-deal Brexit on April 12, May must present a summit of European Union leaders next Wednesday with a plausible strategy to win approval in parliament for the Withdrawal Agreement that she negotiated with Brussels.
Finance minister Philip Hammond said it was an "expectation" that Brussels would offer a longer extension at the April 10 summit than the short one Britain is targeting, but London would want to curtail it as quickly as possible after passing a Brexit deal.
May held talks with the opposition Labour party leader Jeremy Corbyn in an effort to find a way out of the Brexit impasse.
Britons voted to leave the European Union by 52% to 48% in 2016, and the following year British Prime Minister Theresa May gave notice of the intent to leave the bloc on 29 March under Article 50 of the EU's Lisbon Treaty. He himself has said such a vote should be restricted to specific circumstances.
Britain is now due to depart on April 12, but many observers doubt that May will be able to secure backing for her withdrawal deal by then.
In case Corbyn and she fail to reach agreement, May said Parliament would have to vote on a range of choices - and the result would binds the authorities.
The issue of a second public vote rose to the surface after a Labour spokesman said the party would only back such a move to avoid a "Tory Brexit" or no deal.
Any deal that could meet the acceptance of Labour would have to include a customs union - one of the five conditions Corbyn set out in his letter to the prime minister in February.
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May didn't indicate how long an extension she would seek in the EU, although she said she hoped Britain and the agreement could pass at time, by May 22 to prevent engaging in elections to the European Parliament.
Health Secretary Matt Hancock's comments followed similar attacks from Tory MPs furious that Theresa May has begun holding talks with Mr Corbyn to seek a Brexit compromise.
Parliament has voted repeatedly to rule out a "no-deal" Brexit - most recently on Wednesday, when the House of Commons passed a bill that forces the government to ask for a delay to Britain's exit rather than crash out.
"However", May said, "if we cannot agree on a single unified approach, then we would instead agree a number of options for the Future Relationship that we could put to the House in a series of votes to determine which course to pursue".
Common Market 2.0: This so-called "Norway Plus" model was also backed by Labour in Monday's indicative votes, and comes closest to Labour's own alternative Brexit plan.
They warned: "A second referendum would be exploited by the far right, damage the trust of many core Labour voters and reduce our chances of winning a general election", they warned. She has vowed to "fight until the last hour" to avoid a no-deal outcome - something that would hit the United Kingdom s only land neighbour Ireland hardest.
May and Corbyn were to face off at the weekly Prime Minister's Questions in the House of Commons ahead of a likely meeting in parliament during the afternoon.
Arriving for the talks, Mr Starmer confirmed that a "confirmatory" referendum was among the ideas on the table for discussion.
He said: "Yesterday I wrote to David Lidington to say I thought those elections were now essential and have to be held".