At the close, the FTSE 100 index was down 70.7 points, or 1.1%, at 6,044.9.
Sterling dropped 0.2% against the dollar to $1.4231 and fell 0.5% against the euro to â‚¬1.2612.
Meanwhile, the "volatility index" for the pound - a measure of investors' uncertainty - has hit the highest levels since the 2008 financial crisis.
Opinion polls at the weekend suggested the Leave campaign was ahead of the Remain team, and figures from betting exchange Betfair indicate the implied probability of the UK staying in the EU has fallen to 64%, down from 78% a week earlier.
Investors were also cautious ahead of a US Federal Reserve's meeting later this week.
"Financial markets are in a clear risk-off mode once more this week," said Joshua Mahony, market analyst at IG.
"The Brexit-shaped shadow that looms over markets is also joined by a [Fed] meeting this week, which while predictable by action, is less certain by tone. There is a high likeliness that at a time where risks are so high, market sentiment will continue to drive volatility for the next 10 days."
However, Deutsche Bank said a Leave vote would not necessarily hit UK shares. Both the German bank and JP Morgan remained "overweight" on UK shares, helping the FTSE fall less sharply than continental stock markets.
"In the case of a Leave vote in the UK referendum... we expect UK equities to outperform the European market, given the likely [sterling] depreciation in such a scenario," Deutsche analysts said in a note.
Shares in BT Group fell 2.8% after analysts at Berenberg cut its price target for the telecoms giant.
In the FTSE 250, G4S shares fell 5% after it emerged that the gunman responsible for the Florida nightclub massacre was one of its employees.
Ocado was the biggest loser on the 250, down 8.1%, with analysts citing Amazon's expansion into the UK grocery market as likely to provide unwelcome competition for the online food delivery business.
(Close): The FTSE 100 fell and the pound slipped as investors stayed cautious ahead of the UK's EU referendum next week.