Finally, a financial flare-up that the world's central banks will have seen coming.

On Friday morning London time — when the results of a U.K. referendum will show whether the nation has or has not chosen to leave the European Union — the Bank of Japan and the Swiss National Bank's Singapore desk could already be selling yen and francs. They and their peers are also primed to pump liquidity into banks fearful of running dry and to push back against capital flight from sterling. It is what comes later that monetary-policy makers are less ready for.

With the outcome of the British vote too close to judge, central bankers are reaching for measures honed during the last financial crisis to assuage investor nerves. Yet beyond calming words, potentially coordinated among Group of Seven economies, and a flash of action should the U.K. tip markets into panic, the institutions may have little left to offer if the turmoil morphs into long-term downturn.