One of the central claims of the “Leave” campaign was that Britain would no longer have to send 350 million pounds ($462 million) a week to Brussels. Those savings, supporters argued, would be reinvested in the National Health Service and other government programs. Almost immediately after the vote on Thursday, Nigel Farage, the leader of the United Kingdom Independence Party and an early “Leave” proponent, denied even making such a promise, even though he had said as much in a BBC appearance this month.

Even the 350 million pound figure is wrong. Britain’s net contribution to the E.U. budget is 150 million pounds, according to the Institute for Fiscal Studies. And the British government would have to carry out some of the functions now handled by the European Commission, the union’s executive arm, which negotiates trade agreements, enforces antitrust laws and is involved in policymaking in many areas, from agriculture to information technology.

On immigration, “Leave” campaigners like Mr. Johnson, who hopes to replace David Cameron as prime minister, have also changed their tune. They had argued that after leaving the E.U., Britain would no longer have to allow in workers from the union’s other 27 member nations automatically. They promised to impose a points-based system for selecting only highly skilled immigrants. But Mr. Johnson now says, in a column in The Telegraph, that Britons will continue to be able to live, work and travel freely to other European countries, a privilege the E.U. countries will certainly not grant without reciprocity. He also says that citizens of other E.U. countries living in Britain “will have their rights fully protected.”

The backtracking by Mr. Johnson and his allies has exposed the venality and cynicism of their campaign — unfortunately for Britain, far too late.