Amber Rudd believes that a second referendum is more likely than a no-deal scenario if Britain can not strike a Brexit deal with the EU.
The former home secretary told ITV's Peston programme that the UK would find itself in "completely uncharted territory" if it failed to agree a deal with the bloc.
Britain is set to leave the EU on March 29 next year.
Ms Rudd told ITV News Political Editor Robert Peston that the UK may end up with a Norway-style EEA deal, but played down the prospect of a "Canada-style" agreement - something favoured by many Brexiters.
Theresa May has previously claimed that a Canada-style deal would risk breaking up the UK.
Ms Rudd's comments came as Jeremy Corbyn urged Mrs May to strike a "sensible" deal with the EU or "make way" as leader.
Asked if the reality of no-deal would be worse than opting for a second referendum, Ms Rudd replied: "Absolutely".
"I don’t think no deal will happen," Ms Rudd said.
"I think that if we can't get a negotiated deal that the prime minister brings back through parliament then I think that we’re in completely uncharted territory constitutionally..."
She added: "But I do think it would be ironic indeed if we got a people’s vote because the more Brexit-y people in my party were unable to support the Prime Minister in her negotiated settlement and then they might not even get their Brexit.
"So I think they have to think very carefully about the consequences of not supporting a negotiated settlement."
The Hastings and Rye MP said that dozens of Conservative MPs would be willing to vote down a Canada-style deal.
Among concerns over such an agreement is the thorny issue of the Irish border.
Ms Rudd said: "I think there are a number of people, in fact I’ve talked to a few colleagues and I reckon there are conservatively about 40 of us who would not support a Canada type deal.
"But to be frank there are so many reasons a Canada type deal doesn’t work, starting with the Irish border, going on to manufacturing that I think we can make those arguments.
"But that just reinforces the point that there is an impasse if the two wings of our party face up to the fact that we have these elements that differentiate us but the rebel group need to think again because I think we've only got one shot at a negotiated settlement."
Peston is broadcast on ITV at 10.45pm on Wednesdays - but you can watch it live on this page at 8pm as the programme is recorded.