Holidaymakers have stockpiled dollars and euros ahead of the EU referendum and travel money outlets have come close to running out of cash amid the surge in demand.
Concerns that a Brexit vote could hit sterling saw long queues form outside bureaux de change across the country as Britons locked in exchange rates before Thursday's poll.
The Post Office, which processes one in four of all UK foreign exchange transactions, said currency sales jumped 74 per cent year-on-year on Tuesday, with branch sales up 49 per cent, and online demand 381 per cent higher.
Analysts have said the value of the pound could drop by as much as 20 per cent within hours if Britain votes to leave the European Union.
Mike Cooke, chief executive of Currency Exchange Corporation, said it planned to increase stocks of dollar and euro notes by 80 per cent overnight in response to high demand.
"Everybody is buying their foreign currency now, they don't want to wait until tomorrow," he said. "At one stage today we were virtually sold out of euros and dollars at every branch."
The company, which operates 38 branches in London, said they had replenished stocks in anticipation of strong sales on Thursday.
"Most people that come into our stores are going on holiday in July or August and are buying half of what they need now. They're don't want take a chance because if we decide to leave [the EU] the markets are saying that the euro and dollar will get significantly stronger," said Mr Cooke.
Travelex, another major currency provider, said online orders had jumped 30 per cent compared with the previous week, while FairFX said dollar transactions had quadrupled since last week and euro transactions had doubled.
The Post Office said currency sales were up 36 per cent year-on-year in June so far, with the majority of transactions in euros and US dollars.
It stressed that supplies were "read[ily] available" in branches and online despite the surge in demand.
Travelex said online traffic had climbed 20 per cent compared with the previous week in a sign that consumers were closely monitoring exchange rates.
David Swann, head of pricing at Travelex in Europe, said: "Since David Cameron [the Prime Minister] announced the referendum back in February the pound has been on a bit of a volatile rollercoaster against major currencies including the euro and US dollar.
"While we can't say for sure, it's highly possible that this surge is due to the uncertainty being fuelled by the EU vote."
It came as Azimo, the online money transfer service, announced that it would temporarily suspend trading from 6am on Thursday due to "unprecedented circumstances".
"The uncertainty around the result will unfortunately create significant disruption in the currency markets," the company said, adding that the 24 hour move was the "right thing to do" to ensure the safety of customers' cash.
Transferwise has already announced it will suspend transfers in sterling from Thursday until the referendum result is announced on Friday morning.
The Bank of England has warned that the pound could fall "sharply" if Britain votes to leave the EU.
George Soros, the billionaire investor, said the consequences could be more damaging than when he bet against the pound and forced the UK out of the Exchange Rate Mechanism in 1992.
Sterling was flat on Thursday, at €1.30 against the euro and $1.468 against the dollar.