Mr. Johnson wants to engineer a similar takeover of the Conservatives, purifying the party of Winston Churchill and Margaret Thatcher so that it can repel challenges from the hard-core pro-Brexit movement, which now has its own competing party. If he clings to power, a more radicalized Tory party could yet emerge.

But Mr. Johnson offers little to supporters beyond a promise to leave the European Union next month. His other policies — tax cuts, more money for the police, tighter immigration rules — are standard-issue Conservative fare. Several of his rivals for the party leadership this spring ran on substantively similar platforms.

“There’s not much of a quid pro quo there,” said Tim Bale, a professor of politics at Queen Mary University of London.

In fact, Mr. Bale noted, a few of the rebels — notably Philip Hammond, who advocated a policy of austerity as chancellor of the Exchequer in the previous Conservative government — were put off by Mr. Johnson’s profligate spending plans.