In a speech on Monday, the Prime Minister is expected to warn that failure to deliver on the result of the 2016 Brexit referendum would risk '˜catastrophic harm'Â to faith in the democratic process.
In extracts released by Downing Street ahead of the speech, the PM is quoted as saying that the result of the Welsh referendum of 1997 was '˜accepted by both sides', despite being carried by a wafer-thin 0.3% majority.
However, parliamentary records show that Mrs May was among 144 MPs who voted for an amendment which would have blocked the Government of Wales Bill giving effect to the referendum result.
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Also backing the amendment were prominent Brexiteers Liam Fox, John Redwood, Iain Duncan Smith, Owen Paterson, Bernard Jenkin and John Whittingdale.
In 2005, Mrs May stood in the general election under a Conservative manifesto promising a second referendum to decide whether to overturn the 1997 result.
In her speech, the Prime Minister is due to say: '˜On the rare occasions when Parliament puts a question to the British people directly we have always understood that their response carries a profound significance.
'˜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.'
And she will add: '˜I ask MPs to consider the consequences of their actions on the faith of the British people in our democracy.
'˜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.'
But the 2005 Conservative manifesto made clear that the party did suggest that the people of Wales should vote again, stating: '˜In Wales we will work with the Assembly and give the Welsh people a referendum on whether to keep the Assembly in its current form, increase its powers or abolish it.'
Labour MP for Cardiff Central Jo Stevens said the development had exposed '˜yet more utter hypocrisy from the PM, who, with other leading Brexit Tories, voted against legislation giving effect to the result of the Welsh referendum before it was implemented'.
And Cardiff South & Penarth MP Stephen Doughty, a leading supporter of the Best for Britain campaign for a second referendum, said: '˜This is a very strange example for the PM to use - not least given she herself voted against implementing the Welsh referendum result, and the Tories continued to oppose it for years afterwards.
'˜But unlike Brexit - the Welsh Assembly grew in public support after the referendum. Brexit has headed decisively in the opposite direction - which is why the people should have the final say.'
There was no immediate response from Downing Street to a Press Association request for comment.
Wales voted in 1997 for the creation of a devolved assembly by a margin of 559,419 to 552,698 - 50.3%-49.7%. The Assembly was brought into being in 1999.