Promises to quickly reduce immigration levels are also being played down. Migration was the cornerstone of the Leave campaign, which objected to the European Union’s insistence on the free movement of labor, capital, goods and services. Since 2004, when 10 more countries joined the European Union, large numbers of eastern and southern Europeans have moved to Britain for work.

Mr. Johnson argued that it was impossible for the government to reduce immigration while in the European Union. His ally Michael Gove, the justice secretary, said a leave vote would “bring down the numbers” by 2020. Experts have long said that would be very hard to pull off. The European Union has demanded from nonmember states — Norway, for example — free movement of workers in exchange for access to the bloc’s single market.

On Friday, the day after the referendum, Daniel Hannan, a member of the European Parliament and one of the most knowledgeable advocates of Brexit, stunned some viewers of the BBC by saying: “Frankly, if people watching think that they have voted and there is now going to be zero immigration from the E.U., they are going to be disappointed.”

Mr. Hannan wrote on Twitter, “I was for more control, not for minimal immigration.” Facing a backlash, he observed that a lot of Remain voters “are now raging at me because I *don’t* want to cut immigration sharply,” adding, “There really is no pleasing some people.” He then announced that he would “take a month off Twitter.”