Sterling fell 1 per cent against the dollar to hit a three-week low on June 6.
Against the dollar, sterling fell to $1.4370, recovering slightly from lows of 1.4352 in early trading in Asia, its lowest in three weeks.
The euro was 0.75 percent higher at 78.95 pence.
Currency traders are expecting a rocky month for the pound.
One-month sterling volatility, which gives a measure of how much the pound will swing during the referendum date, jumped to 21.9, the highest since the depths of the financial crisis in February 2009.
YouGov asked people to judge whether they thought the UK should leave the EU if they were £100 a year worse off afterwards.
The majority (44 per cent) of people said they would vote to leave, while 42 per cent said they would remain.
Connor Campbell, Spreadex financial analyst, said that the pound was continuing to feel the ragged to-ing and fro-ing of the duelling EU referendum campaigns.
"The most recent downward movement was sparked by a series of polls over the weekend that suggest the Brexiters have gained ground as immigration has come into focus, reintroducing a wave of uncertainty that appeared to have been put to bed in light of the 13-point lead Vote Remain had around a fortnight ago," he said.
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Currency traders are nervous about the EU referendum on June 23 because of its potential to hit the value of sterling.
Christine Lagarde, managing director of the International Monetary Fund, has said the pound could lose as much as 20 per cent of its value if the UK votes to leave.
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