The Post Office, which deals with a quarter of foreign exchange transactions, said that sales had seen a 74% rise since the weekend, while foreign exchange broker HiFX also saw an increase in demand for dollars and euros of 50%.
Use of exchange website FairFX.co.uk also surged by more than 300% in a week, the newspaper said.
The value of the pound post-Brexit has been a key battleground for the Leave and Remain camps as both try to convince voters, who go to the polls today (June 23), to back their campaigns.
Sterling has recovered in recent days after suffering two-month lows against the dollar and the euro a week previously.
Economists are expecting the pound to fall in value if the UK chooses to leave the EU today with HSBC predicting a 15% to 20% drop against the dollar after a Brexit.
Founder of MoneySavingExpert.com, Martin Lewis, told the newspaper that consumer fears of having “less bang for their buck” while abroad was fuelling the panic-buying. “We’ve been swamped with people panicking about what’ll happen to their holiday money,” he said. “The markets don’t like uncertainty, so that alone likely means that in the event of an out vote the pound would weaken, meaning people would get less bang for their buck when going abroad. On the other hand if it is an in vote the pound is likely to rally, which means people who are buying in advance could be losing out.”