On the eve of the Brexit vote, I suggested to a friend of Prime Minister David Cameron’s that the PM should perform a volte-face, as had his predecessors Winston Churchill and David Lloyd George on various occasions. He would explain that his attempt to renegotiate Britain’s position in the EU, to satisfy the legitimate concerns of his people, had been stiff-armed and that, despite the grave risks, he had decided to endorse the Brexit after all.

I was informed that Brexit would be overwhelmingly defeated and my idea was idiotic. After the vote for independence, Mr. Cameron announced his intention to resign, saying he would do everything he can “to steady the ship”, but that it wouldn’t be “right for me to try to be the captain that steers our country to its next destination.”

With all due respect, he’s wrong.

Think back to, say May 28, 1940. It was 18 days after Churchill’s appointment as Prime Minister. He rose before the Commons to address the King of Belgium’s unilateral surrender to Nazi Germany the day before. “The situation of the British and French Armies…is evidently extremely grave. The surrender of the Belgian Army in this manner adds appreciably to their grievous peril…the House should prepare itself for hard and heavy tidings.” On June 4, in the wake of the evacuation of the British Expeditionary Force from Dunkirk, he rose again to say “Wars are not won by evacuations.”

Did he then announce that he was no longer the man to steer the ship of state, and resign? No. What he said was: “We shall go on to the end, we shall fight in France, we shall fight on the seas and oceans, we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be, we shall fight on the beaches, we shall fight on the landing grounds, we shall fight in the fields and in the streets, we shall fight in the hills; we shall never surrender…”

Britain and its allies went on to win World War II.

Granted, Europe isn’t the Third Reich and Mr. Cameron isn’t Churchill, or even Margaret Thatcher, but Britain needs David Cameron. Even those who favored Brexit cannot deny that it is risky and that a great deal of hard work will be required to preserve, much less enhance, Britain’s economic well-being and security. David Cameron, on balance, has done a great job as Prime Minister, delivering one of the best recoveries in the EU from the crisis of 2008-9. On many things, he has been a great friend of America.

He should buck up. On the eve of the vote, over 85 Conservative MPs signed a letter of support for him as Prime Minister. They included Boris Johnson, the former Mayor of London, a leading voice for Brexit and a mooted successor. To whom is Mr. Cameron going to hand off? To George Osborne, his Chancellor of the Exchequer? No longer: Osborne threatened to raise taxes and harm pensioners if Brexit prevailed. To Boris Johnson, who has never held a Cabinet post? To UKIP’s Nigel Farage? To Jeremy Corbyn, the Labour Party leader who’s a throwback to the nineteen-thirties and to the left of even America’s Bernie Sanders and Elizabeth Warren?

Mr. Cameron promised to ask Britons for their opinion, and he kept his promise. It wasn’t a “blunder”, as some have said, it was honor. Bravo. And he gave his own opinion, with, as he said Friday, his usual passion. He also said in his resignation statement: “We should be proud of the fact that in these islands we trust the people for these big decisions.” Now that they have spoken, Mr. Cameron can prove he meant that.

Britain needs him more than ever to steer the country through the choppy waters he himself foresaw. Would he really rather leave the job to a lesser man? Surely he can’t truly want his predictions of doom to be proven right?

This isn’t the time for discouragement or — dare it be said — petulance. Mr. Cameron can, indeed must, do this. The Prime Minister is the steward of a noble political tradition with a lineage of more than a thousand years. The United Kingdom is the fifth largest economy in the world, and it has just freed itself of an EU dominated by a bureaucracy of upstarts. What an opportunity for Mr. Cameron to carry on. You’ve been given the rudder, man, sail her!