At a time of deep political and economic anxiety, the contest is producing the surreal experience of something that feels like democracy — an election campaign season, complete with televised debates and policy announcements — but without any public franchise. In this case, the “electorate” consists of a mere 160,000 people, just 0.3 percent of the national electorate, who are significantly older and richer than average. And while Mr. Johnson is hounded by questions surrounding his honesty and indiscretions — questions that might damage him in a nationwide contest — the Conservative Party membership seems to view his personality as an asset.

This is uncharted territory. Conservative Party rules have changed since Mr. Major entered office in 1990, to allow the members to have the final say. (Mrs. May’s rivals all withdrew in 2016, so the members weren’t consulted.) At first glance, a leader elected by 160,000 people might seem to have a greater democratic mandate than one appointed by their own colleagues. But as more becomes known about the unusual identities and priorities of the party members, the worry is that Britain is now in the grip of something combining the worst aspects of both oligarchy and representative democracy. It might best be described as unrepresentative democracy.

Mr. Johnson’s appeal to his base rests heavily on his enthusiastic comments about “no deal” Brexit, a kamikaze policy that would devastate Britain’s economy and produce a state of emergency for basic civil infrastructure, such as the supply of medicines. It would, however, signal a complete rejection of the authority of Brussels, which is why Mr. Johnson toys with it. The fact that a clear majority of the public opposes the idea is, for now, irrelevant.

More disturbingly, new polling suggests that Conservative Party members are now so fixated on Brexit that they believe it is worth doing at almost any cost — even if it leads to Northern Ireland or Scotland leaving the United Kingdom, “significant damage to the U.K. economy” or, most strikingly , the destruction of the Conservative Party. For the next few weeks, the most influential force in British politics is a fanatical sect.

How did Britain reach this extraordinary situation? A plausible part of the explanation is that the Conservative Party has been heavily infiltrated by supporters of Nigel Farage, the far-right populist who formerly led the U.K. Independence Party and who recently established the Brexit Party. His new party took more than a third of the vote in May’s European Parliament elections, energized by the fact that Britain did not leave the European Union on the scheduled date of March 29.