At the close, the FTSE 100 was down 121.44 points at 5,923.53.
On the currency markets, sterling fell 0.8% against the dollar to $1.4152 and was flat against the euro at â‚¬1.2612.
In a further sign of market nerves, yields on UK government bonds fell to record lows.
Returns on 10-year UK government bonds fell by a significant amount - 0.06 percentage points - to a record low of 1.146%, while 20-year and 30-year "gilts" also dropped to record lows.
Polls have indicated the Leave camp is ahead of the Remain campaign, and the betting odds on the UK leaving the EU have narrowed.
"Panic appears to be gripping markets as the headlines fill up with references to a possible Brexit, with the Sun's declaration for Brexit emblematic of the worry that the Remain campaign has lost a crucial segment of the population," said Chris Beauchamp, senior market analyst at IG.
Shares in housebuilders fell, despite FTSE 250 member Crest Nicholson reporting a 25% rise in half-year pre-tax profits to Â£72.6m.
Crest Nicholson shares fell 7%, and among other housebuilders Berkeley Group dropped 4.2% while Barratt Developments was down 3.7%.
Shares in Go-Ahead Group dived 18% after the transport group warned that profit margins at its Thameslink franchise were likely to be half of what it had originally forecast.
The firm cited "very challenging performance and industrial relations environments" at its Govia Thameslink Railway unit, adding that profit margins over the life of the contract "are now more likely to be nearer to 1.5% than the 3% previously expected".
Shares in Ocado fell 2.9% as investors worried that the online grocer will be hit by Amazon's launch of its own online supermarket service.
(Close): The FTSE 100 index dropped below the 6,000 level for the first time since February and the pound fell as markets remained nervous ahead of the UK's referendum on EU membership.