Ms May managed to placate some critics in the Commons and Lords by promising Parliament a vote on the Brexit terms she agrees, but sources indicated the country will leave the bloc even if her particular deal is rejected by MPs and Peers.
Such a move would probably mean the hardest kind of Brexit, with the UK leaving the EU without any successor agreement and reverting to World Trade Organisation rules - meaning MPs could be more likely to back whatever terms Ms May manages to achieve.
The landmark speech also saw the Prime Minister announce that the UK would leave the single market and try and negotiate a new free trade agreement with the European Union from the outside.
Addressing diplomats at Lancaster House she said: "When it comes to Parliament, there is one other way in which I would like to provide certainty.
"I can confirm today that the Government will put the final deal that is agreed between the UK and the EU to a vote in both Houses of Parliament, before it comes into force."
Government sources later said that the Prime Minister was "clear, we are leaving the EU" when asked what would happen if Parliament rejected the deal Ms May strikes.
The Prime Minister was also unequivocal in her speech, while urging EU leaders to strike a mutually-beneficial deal with the UK, that she was not afraid of leaving the bloc without any deal at all.
She said: "I am equally clear that no deal for Britain is better than a bad deal for Britain."
At the end of last year a leaked Treasury document warned Britain could lose up to £66bn a year if it pursues a hard Brexit option of losing access to the single market and leaving the EU customs union.
The Government's figures suggested the UK's gross domestic product could fall by as much as 9.5 per cent if it leaves the EU and reverted to World Trade Organisation rules.
One Tory said: "At the moment most people are pleased that the Commons has been given a vote on the deal.
"But what Theresa May has offered is a choice between on one hand, whatever she puts forward, or on the other most costly, unattractive type of Brexit. It might not be much of a choice."
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