Finally, the Union’s foreign and security policy would suffer a severe setback. It is easy to mock the current approach, which has little to show for itself. But one only has to look at the Union’s unstable neighborhood — Ukraine and Russia to the East, North Africa and the Middle East to the south — to appreciate that it is going to need to get serious in the next decade or so. Without Britain, the bloc would have less clout.

So how can European leaders cut the risk of Brexit?

For a start, Mr. Cameron needs to play the European Union diplomacy game better. That means quickly making peace with Mr. Juncker. Why not invite him to Downing Street? The prime minister should also propose a heavy hitter as Britain’s own European Union commissioner — somebody like William Hague or Michael Howard, both former leaders of his party.

Meanwhile, Mr. Cameron needs to build more alliances. He made the error of relying too much on Chancellor Angela Merkel of Germany. Britain also needs allies in Italy, France, Spain, Poland and other nations.

The other Union leaders offered Britain a couple of concessions at the summit meeting last week. They said they would review the system of nominating future commission presidents. This is important because the way in which Mr. Juncker was chosen amounted to a power grab by the European Parliament. The leaders should make clear that this will not set a precedent.

The summit meeting also interpreted the phrase in the European Union treaty calling for ever closer union among the peoples of Europe as “respecting the wish of those who do not want to deepen” integration any further. That formulation will not satisfy British euro-skeptics, for whom the phrase is a bugbear. But with a few tweaks. this olive twig could become a full olive branch.

If Mr. Cameron does propose a heavy-hitter as Britain’s commissioner, other leaders should respond by offering that person a top job.

They should also sharpen up the work program they have sketched for the next five years. The core of this should be: a renewed drive to complete the single market; free trade deals with the United States and Japan; a revamped energy policy; building up nonbank finance so it can take up the slack as banks shrink; and cutting regulations.