Conservative leader Mrs May has granted Tory MPs a free vote.
Its chief negotiator Michel Barnier said the European Union "cannot go any further" in trying to persuade MPs to back the agreed terms of exit and the United Kingdom had to break the impasse.
Dr Wollaston added on her second referendum proposal: 'For young people in this country, they face being wheeled into the operating theatre for major constitutional, social and economic surgery based on a consent form that was signed by their grandparents almost three years ago'.
Tory former Brexit minister Steve Baker said he was "very confident" there won't be a general election.
At a meeting of senior ministers on Thursday, a Cabinet source said Mrs May made clear she was "less than impressed with (the) Remainers" and "demanded more loyalty".
"Again the House of Commons says what it doesn't want", Mr Barnier told the European Parliament. It should be noted that the votes are not legally binding and a no-deal Brexit on March 29 is still a possibilty unless the two sides reach a deal.
Shadow business secretary Rebecca Long-Bailey told BBC News Parliament would increasingly "set the agenda" if the government was not in control of events.
Sarah Newton, a junior work and pensions minister, resigned after defying the prime minister to block a no-deal exit. To take no deal off the table, it is not enough to vote against no deal - you have to agree to a deal.
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A No 10 spokesman said she did not discuss resigning after her latest defeat because her government had recently won a confidence vote in the Commons.
Some of them believe it's time now to go hell-for-leather to leave without an overarching deal but move to make as much preparation as possible, and fast.
'The Government is in real problems because they are trying to fool the people into somehow believing that somehow or other the deal she has offered is the only one that is available'.
Discussions with the DUP are ongoing, but no formal decision on the next vote has yet be announced. The lawmakers then supported the idea of replacing the backstop provision, which has caused the most controversy in parliament, with alternative arrangements.
Labour's Hilary Benn, pushing the cross-party amendment, said he was not seeking to specify what MPs should do next but instead "book a slot" to allow a debate on how to resolve Brexit.
The government also announced it will not introduce any new checks or controls, or require customs declarations for any goods moving from across the border from Ireland to Northern Ireland if the United Kingdom leaves the European Union without a deal.
Under a temporary scheme 87% of imports by value would be eligible for zero-tariff access - up from 80% at present.