In a speech on the eve of a crucial vote in the House of Commons on her deal with Brussels, the Prime Minister will ask the public to imagine if Westminster had rejected the outcome of votes that created the Scottish Parliament and Welsh Assembly.
It comes as opposition MPs published draft legislation for a fresh referendum that would give voters the chance to reverse Brexit.
With less than 36 hours to go until the vote, Mrs May will warn that parliament is more likely to block Brexit than allow Britain to crash out of the EU without a deal.
However, while a small number of Conservative Brexiteers have now said they will back her deal to ensure that Brexit is delivered, the government is still expected to fall to a heavy defeat.
Warning of “catastrophic harm” to public trust in politicians if Brexit isn’t delivered, Mrs May will “ask MPs to consider the consequences of their actions on the faith of the British people in our democracy”.
The Prime Minister is expected to say: “Imagine if an anti-devolution House of Commons had said to the people of Scotland or Wales that despite voting in favour of a devolved legislature, Parliament knew better and would overrule them, or else force them to vote again.”
Mrs May will add: “When the people of Wales voted by a margin of 0.3%, on a turnout of just over 50%, to endorse the creation of the Welsh Assembly, that result was accepted by both sides and the popular legitimacy of that institution has never seriously been questioned.”
The Prime Minister will say that while the two sides in the 2016 referendum disagreed on many things, they were united on one thing – that “what the British people decided, the politicians would implement”.
Four Brexiteer backbenchers announced on Sunday they will back the Prime Minister’s withdrawal agreement.
One of the four, Sir Edward Leigh, said it was “now inconceivable that this Parliament, and this Speaker, will allow the UK to leave on WTO terms on March 29.
“Therefore my message to my fellow Brexit-supporting MPs is you are playing with fire if you vote down this deal in the hope of something better, and the only way to deliver Brexit is to vote for the deal this week.”
Legislation to bring about a second referendum has been published by a cross-party group of anti-Brexit politicians, including representatives from Labour and the Conservatives.
The draft bill recommends that the public be asked whether they want to remain in the European Union or leave under the Prime Minister’s deal.
Organisers note that Article 50 would have to be extended in order for another poll to take place, meaning the UK would remain a member of the EU beyond March 29.
The legislation could be introduced through the House of Lords under plans being considered by the group, which also includes SNP Westminster leader Ian Blackford.
It recommends the ballot paper be worded: “Should the United Kingdom remain a member of the European Union or leave the European Union on the negotiated terms?”
Tory former attorney general Dominic Grieve said the bill provides the Government with an “escape hatch” if there is no majority in Parliament for Theresa May’s deal or no deal. “This Bill provides a legally credible way forward, and a politically credible way forward,” he added.
Mr Blackford said MPs had a “responsibility to present an alternative route to protect our economy and citizens rights”. He said: “Scotland voted overwhelmingly to remain in the EU and the SNP believe this Bill is an effort to build a consensus across the house for a second EU referendum.”
The group has also drafted a ‘Paving Bill’ designed to enable the Electoral Commission to start the necessary consultation around a referendum question and lead campaign designation.