More than 76,000 options on the Ftse 100 Index changed hands on average each day this month through the end of last week, the most in six years.
Traders are pricing in a 20% jump in UK equity volatility through June.
With Bank of England governor Mark Carney saying this month that leaving the EU could lead to a UK recession, global fund managers have become even more wary of a market that was already their least favoured.
Their allocation to the UK’s equities has fallen to the lowest levels since 2008, according to a Bank of America survey published last week.
“Investors are extremely anxious about Brexit,” said Guy Foster, the head of research at Brewin Dolphin in London.
“Nobody wants to own anything UK-facing going into the referendum.”
Even as polls suggest the campaign to remain in the EU is winning, the Bank of America report showed that investors consider the issue the biggest tail risk in the world.
Sterling, whose plunge this year has helped make the Ftse 100 one of the region’s best-performing gauges, is near the most undervalued it’s ever been, the note said.
“There are many people who, even if you told them the outcome of the vote, don’t know what the impact will be,” said Ben Kumar, an investment manager at Seven Investment Management in London.
“There is no consensus, and it’s very difficult to position most portfolios for that,” he said.
A measure of Ftse 100 volatility expectations has jumped almost 40% since March, while actual market swings have dropped.
Eight of the 10 most-owned options on the index are bearish.
Bank of England officials have said the weakening economy may not be due only to Brexit concerns.
A report last week revealed signs of cooling in the labour market, with job creation in the first quarter running at a fraction of the pace seen at the end of 2015.
Credit Suisse said the following day that investment and employment decisions being postponed until after the June 23 vote partly explain the slowdown.
Morgan Stanley warned UK and European equities could fall as much as 20% in the event of Britain exiting the union.