Johnson was speaking Wednesday at a closed-door meeting with Conservative activists, the BuzzFeed news website reported Thursday, citing a leaked audio clip.
"You’ve got to face the fact there may now be a meltdown. OK? I don’t want anybody to panic during the meltdown," he told the gathering at a private dinner.
Johnson, who is pro-Brexit, said Prime Minister Theresa May was "going to go into a phase where we are much more combative with Brussels. "It’s going to be all right in the end," he promised.
In a separate comment on North Korea, the British foreign minister claimed his country appeared to have leverage on the reclusive Communist state and floated the idea of visiting it some time.