The Tory grandee said a re-run of the 2016 vote was the most likely outcome of the Brexit deadlock.
But he predicted a fresh referendum would be a "tragedy" because it would distract politicians from focussing on the country's real problems.
Lord Hague, who was Foreign Secretary under David Cameron, is understood to be close to Theresa May.
He is a strong supporter of her Brexit deal – and warned that its defeat last week was "calamitous for British democracy".
The former Tory leader wrote in the Daily Telegraph: "At a stroke, the majority of MPs joined together to paralyse the only good government available, make Brexit impossible to deliver on schedule or even at all, and produce in much of the population an utter disgust with their proceedings.
MPs have started the countdown to another referendum
"Most important of all, wittingly or not, they started the countdown to another referendum."
Lord Hague claimed the PM's deal "cannot be passed" and said there is no time left to negotiate a better one.
He added: "What about some cross-party agreement on a new plan? Theresa May offered this in recent days but has inevitably had to turn away from it."
The top Tory predicted politicians would evenutally conclude: "Oh go on then, let's ask them again."
Remainers have stepped up their campaign for a second referendum since Mrs May's historic Commons defeat last week.
Conservative MP Guto Bebb said: “Even William Hague acknowledges that a people’s vote is the most logical outcome.
“When every route to Brexit has been examined and exhausted, it will become clear there is only one way forward – to hand the final decision back to the British public through a people’s vote."
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