LONDON — Prime Minister Boris Johnson says he will not do business with Parliament until the opposition Labour Party agrees to a general election. Labour says it will not agree to an election until the European Union decides how long an extension to grant Britain to leave. And European leaders say they will not make that decision until the deadlock in London is broken.

Even by the wheel-spinning standards of Brexit, there was something remarkable about the circular futility of events on Friday.

Twelve-hundred nineteen days have passed since the British people voted to leave the European Union, and Britain’s departure now seems more of a mirage than ever. The destination looms on the horizon but eludes every effort to reach it, as Britain’s politicians wage a kind of forever war over how, or even whether, to carry out the results of that much-disputed referendum.

With Mr. Johnson and his opponents locked in their umpteenth standoff this week, the debate drifted farther and farther away from the best way to negotiate Britain’s departure — let alone the costs or benefits of doing Brexit — and more toward a crude display of political positioning in advance of a likely election.