This means that those 40,000 new Tory members suddenly have a say in deciding the country’s fate.

How many of them have come from other parties or harbor competing loyalties is largely a mystery to Conservative leaders. Mr. Rawlins, for instance, flirted this spring with the Brexit Party, the Conservatives’ newest rival, which has become popular with a huge number of longtime Conservatives. He even applied to run as the Brexit Party’s candidate for Parliament in his area, vying to contest a seat now held by a prominent Conservative lawmaker, David Gauke.

But as a group, new members appear to lean toward Mr. Johnson, who has pledged to carry out Brexit by Oct. 31, no matter what.

Polling earlier in the contest found that more than half of Mr. Johnson’s supporters in the party had joined after the 2016 Brexit referendum, and he has courted the right by hinting that he might try to override Parliament to bring about a no-deal Brexit, despite warnings of potential economic calamity.

Though Mr. Rawlins left the party, many newcomers are staying, and whether the Conservatives remain a broad church or become a club for dedicated supporters of Brexit will in part shape the future of British politics.

“The Conservative Party, famed for 150-plus years for its pragmatism, has effectively become an ideological party, or at least its members have,” said Tony Travers, a professor of government at the London School of Economics. “Even if you do have a reasonable filter, you can’t stop a party being shifted quickly in one direction or another by individuals whose views are significantly to one side of its median policy position.”

As it stands, almost anyone willing to pay the 25 pound annual membership fee — about $30 — can join, and while local party officials do cursory internet searches on applicants’ names, they do not tend to bar people merely for dabbling in rival parties. That can create difficult questions for a political system dominated by two parties, in which joining either the Conservatives or the opposition Labour Party can give voters vastly disproportionate power.