Government officials have warned that a no-deal exit could clog ports, starve factories and disrupt supplies of food and medicine. At a cabinet meeting before Christmas, Gavin Williamson, the minister of defense, agreed to put 3,500 troops on standby. The environment minister, Michael Gove, on Thursday warned farmers that British exports to the European Union could be subject to 40 percent tariffs, and that inspections could cause delays, posing a threat to small farmers.

A government publicity campaign will begin next week, as Parliament prepares to vote on Mrs. May’s withdrawal agreement, warning Britons of what to expect if the country leaves the European Union without a deal.

But 76 percent of Conservative party members contacted for the poll dismissed those warnings as “exaggerated or invented,” and 64 percent maintained that a no-deal exit would have a positive rather than a negative effect.

“In some ways, what we see is a kind of repeat of what we saw under David Cameron, which is a leadership unable to convince its own members to back the party line,” said Mr. Bale, referring to the former prime minister.

The risks of a no-deal exit, he added, had been played down by right-wing news outlets like the Telegraph and Express tabloids, and by “the celebrity politicians so many of them admire.” The government itself has walked a fine line on projecting the fallout, trying to simultaneously warn the public of danger and reassure it that the state is prepared.

And there are diverging views within the party about what a no-deal exit would look like, with some lawmakers speaking of a “managed no-deal” that includes a two-year transition period, or a “mitigated no-deal” in which smaller deals are in place to cover key trade areas.

The same survey found equally strong but opposing views among members of the Labour Party. In a poll of 1,035 members, 72 percent said they want the Labour leader, Jeremy Corbyn, to support a second referendum on European Union membership. Mr. Corbyn himself is a longstanding critic of the European Union, and has seemed reluctant to take that step.

Among Labour members, 89 percent said they believed a no-deal Brexit would have a negative impact on the economy in the medium-to-long term. And 82 percent said that warnings of severe short-term disruptions, such as food shortages and price increases, were realistic, as opposed to 35 percent of the electorate as a whole.