The pound has tumbled this year, falling as low as $1.4089 in June before recovering to as high as $1.4842 during the Wednesday U.S. session, its high so far this year, after recent opinion polls started to indicate the remain camp held a tenuous lead.
"A leave vote would come as something of a shock," given the market appeared to be leaning toward pricing in a remain vote, Sarah Hewin, head of research for Europe at Standard Chartered, told CNBC's "Rundown."
Her bank's forecast was for the pound to drop to the low $1.20s if the leave camp won, but rise to the $1.50s on a remain vote.
But she added, "We would expect, whatever the outcome is going to be, a lot of volatility over the next 24 hours."
In addition to the U.S. dollar, other currencies viewed as safe havens would likely see a rush of fund flows.
The yen has already rallied this year, much to the consternation of the country's policy makers who tend to prefer a weaker currency, in part to bolster exports.
The dollar was fetching more than 111 yen at the end of May, but amid the yen's surge, it was only at 104.62 yen at 10:44 a.m. SIN/HK.
Nomura forecasted in a note Wednesday that the dollar-yen pair would fall as much as 4 percent if the leave camp wins. It's expecting a bigger move against the pound, expecting the pound-yen cross would fall nearly 14 percent, compared with expectations the euro-yen cross will depreciate by around 7 percent.
The euro was fetching 118.63 yen at 10:51 a.m. SIN/HK, down from as high as 123.82 yen in late May. The pound was fetching 154.78 yen at 10:53 a.m. SIN/HK, down from as much as 163.86 yen in late May.
Another safe-haven currency likely set to appreciate in the wake of an exit would be the Swiss franc.
Capital Economics forecasted in a note Wednesday that the franc would likely head toward parity against the euro in a Brexit.
The franc was fetching 0.9186 euro at 10:54 a.m. SIN/HK.
Capital Economics said upward pressure on the franc could exceed the 10 percent the currency faced during the 2008-09 financial crisis as Switzerland didn't join the European Union, which increases the perception that the currency offers a shield from concerns that a Brexit would spur other countries to exit the bloc.
Hit to the euro
That concern that a Brexit would unleash a rush for the door would likely weigh the euro as well, analysts said.
Goldman Sachs said a Brexit is a "clear catalyst" for the euro to fall, although it noted the euro might initially rally against the dollar as a risk-off move spurs funds to repatriate.
"A Brexit vote would be a material, negative confidence shock to a region that is struggling to reflate," Goldman said in a note Wednesday.
"We think this would allow 'doves' on the European Central Bank (ECB) Governing Council to shift back into proactive mode and pursue more activist monetary easing, setting the stage for a resumption of the Euro downtrend," it said.
On the upside, the Australian dollar has climbed against the greenback this month and to a lesser extent against the pound.
The Australian dollar was fetching $0.7521 at 11:46 a.m. SIN/HK after trading as low as $0.7171 in late May. Against the pound, the Aussie was fetching 0.5079 pound at 11:47 a.m. SIN/HK, compared with as little as 0.4869 pound in late May.
In the event of a Brexit, Commonwealth Bank of Australia expected the Aussie will fall around 2.5 percent or more against the dollar, while rising as much as 8.3 percent against the pound. The bank noted that volatility in the Aussie-pound cross was as high as during the 2010-2012 Eurozone debt crisis.
"We don't believe markets are appropriately pricing the downside risk to Australia dollar-U.S. dollar pair, given we anticipate global equity and commodity markets declines will lead to a reassessment of the global economic growth outlook, and the fact the referendum results will be released in the less-liquid Asian time zone," it said in a note last week.
There's one emerging-market currency that may hold up in a Brexit: China's yuan, which is pegged to a trade-weighted basket of currencies.
With marginal exports from China to the U.K., the pound is just a low single digit percentage of the basket, Dominic Schnider, head of Asia-Pacific foreign-exchange at UBS Wealth Management, told CNBC's "Squawk Box," adding that even a 10 percent move in sterling wouldn't affect the yuan much.
But if a Brexit left the euro hamstrung, that would have a bigger effect on the basket, he noted.
While that would push up the dollar-yuan pair, "I think the yuan is going to hold up better than other currencies in a risk off environment," Schnider said.
—Alexandra Gibbs and Arjun Kharpal contributed to this report.