The international trade secretary said the extraordinary events in parliament on Tuesday, in which the government suffered historic defeats on Brexit, were an insult to voters.
"I think there is a real danger that the House of Commons, which is a natural remain majority, may attempt to steal Brexit from the British people, which I think would be a democratic affront," he told MPs on the international trade committee.
Theresa May's authority was severely dented on Tuesday night after the Tory rebel Dominic Grieve won backing for an amendment on the EU Withdrawal Act.
It means parliament now has more than just a vote on May's deal. It also has a chance to amend a "plan B" she must bring before parliament in the event of a defeat next Tuesday.
Fox has continued to urge support for May's deal and said it was imperative parliament delivered the referendum result. "I think we have to leave the EU because we have been instructed to do so by the British people," he said.
"Parliament did not give the British public consultation. We contracted out our sovereignty on that particular issue to the British people. We said you take the decision whether we stay in the EU or not."
Questioned about the Irish border backstop clauses in the withdrawal agreement, he said it was not something anybody wanted to see triggered.
All parties wished to avoid it and the only way to do this was to forge ahead and seal the future trade deal that would obviate the need for the Irish backstop, he said.
He also made a point of mentioning the nationalist community in Northern Ireland and said it was not just Democratic Unionist party voters who needed protecting in the Brexit settlement.
"It's just worth considering that the backstop isn't just for the Irish Republic, but also necessary for the reassurance, I think, for the moderate nationalist community in Northern Ireland. I think for them to understand there is no possibility of a return to the hard border is part of the way we underpin the stability of the union."
Northern Ireland voted 56% for remain, after the DUP led the pro-Brexit campaign backed by the then Northern Ireland secretary, Theresa Villiers.
Fox echoed the attorney general, Geoffrey Cox, by describing the backstop as "a calculated risk", warning that the worst possible outcome would be to remain in the EU, and the only way to get a deal over the line was to agree to an insurance policy for the Irish border.
He repeatedly ducked questions on whether the government had a plan B if May lost the parliamentary vote next Tuesday.
He said the very existence of the backstop would help expedite a trade deal. "The backstop is not something we want to see, that either want to see. I see it as an incentive to get an agreement before we ever get there," he added.
The Tory MP Marcus Fysh accused Fox of being naive. It was "monumentally stupid" to think Britain could ever get out of the backstop, he said.
"The calculated risk is a bit like putting five bullets in the chamber of a revolver and playing Russian roulette. It is utterly stupid."
Fox replied: "There are those on the other side of this negotiation who think that what's been negotiated gives Britain an unacceptable advantage. I know some of us find that difficult conceptually to grasp."
Fox added that the "bigger danger here was the political one", which was "not leaving the EU".
The chair of the committee took the unusual step of issuing a statement on Fox's evidence, accusing him of being in denial over Brexit.
"We have come to crunch time in relation to Brexit - with the withdrawal agreement vote just days away. Despite this, Liam Fox's appearance before my committee this morning showed he is still in denial - about the need for government to have a plan B, about the realistic prospect of the UK securing continuing application of EU free trade agreements after Brexit, and about the implications of the backstop on future UK trade policy," said Angus Brendan MacNeil, a Scottish National party MP.
Earlier, Fox said there was an "understandable reticence" among some third countries to press the button on trade negotiations until they knew what deal the UK had secured with the EU.
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