Some £65bn either left the UK or was converted into other currencies in March and April - the fastest rate since the financial crisis in early 2009.
The figures, published by the Bank of England in its monthly register of banking statistics, represent the first evidence of capital flight from the UK - where money rapidly flows out of a country in response to concerns over economic instability.
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The Bank of England figures, which measure flows of cash in and out of sterling, are volatile but have deteriorated dramatically recently.
In the six months to the end of April, some £77bn left the sterling system.
That compares to a fall of just £2bn in the six months to the end of October 2015.
In March, the first full month of the referendum campaign after Boris Johnson joined the Leave campaign, the outflow was £59bn - the second biggest single-month fall since records began.
Although the numbers could be influenced by a number of other factors - such as changes in the balance of payments and appetite for other currencies - economists said that it is clear that they are being primarily driven by concerns about the referendum.
Simon Ward, chief economist for Henderson Global Investors, said: "Investors are obviously concerned that in the event of a Brexit, the economic outlook will be very uncertain - investors dislike uncertainty - so they want to reduce their exposure to the UK equity and bond markets to reduce that risk."
The Bank of England itself has warned repeatedly about the economic risks posed by a possible Brexit.
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