The former Tory Party leader warned the PM of possible party chaos should she fail to deliver on key Brexit promises such as Britain's withdrawal from the EU customs union.
Theresa May repeatedly pledged to take the county out of the European Union's free trade area but some Brexiteer fear the PM could seek to enter an arrangement very similar to the one currently in place.
Mr Duncan Smith said: "The party would split dramatically if that was the case.
"That is just my estimation of it because it was always clear at the time of the referendum.
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"You have got to remember the Government at the time said, and the Remain campaign, ‘if you vote to leave, you must leave the customs union and the single market.’ Seems to me there would be no point in voting to Leave if you didn’t do those things.
"You might as well be in. It’s the