By Jemima Kelly

LONDON, April 7 (Reuters) - Sterling fell to its weakest level in almost 2-1/2 years against a basket of currencies on Thursday, with demand sapped by persistent concerns that Britain could vote to leave the European Union in a referendum in June.

The cost of hedging against big falls in sterling's exchange rate against the euro over the next three months soared to a seven-year high. The price for hedging sterling/dollar volatility jumped above 16 percent for the first time in six years.

"It's the same old story. We don't see any demand for sterling from buyers, and the reason is Brexit," said Credit Agricole currency strategist Manuel Oliveri.

Investors were given a reminder last week of just how exposed Britain might be if foreign investors are deterred by the prospect of Brexit, with an already-hefty current account deficit swelling to 7 percent of GDP in the final quarter of last year.

Sterling fell by as much as half a percent on Thursday against Europe's single currency to a 22-month trough of 81.17 pence per euro. Against the dollar it fell 0.4 percent to $1.4073 .

Those losses helped drive the pound to its weakest since November 2013 against the Bank of England's trade-weighted basket of currencies, having fallen almost 12 percent since late last year.

Subdued risk sentiment was another reason for sterling weakness, added Credit Agricole's Oliveri. The pound tends to be one of the most sensitive among developed currencies to risk because Britain relies on huge investment flows to balance its deficit, which dry up when risk appetite sours.

The latest opinion polls on the EU referendum show the "In" and "Out" campaigns neck-and-neck, while bookmakers' odds point to a roughly 33 percent chance that Britons will vote to leave.

Prime Minister David Cameron, who wants Britain to stay in the EU, is expected to urge young Britons to make sure they vote in the referendum on June 23, warning that leaving the bloc would hit them the hardest.

"The vote could still go either way (and) investors haven't forgotten the massive miss in the 2015 general election forecasts," wrote Rabobank strategists in a research note, referring to the failure of polls to predict a victory for Cameron's Conservatives.

"Tellingly, the 'Poll of Polls', which is a moving average of the six most recent polls, now projects a 50/50-split. It's either In... or Out."

(Editing by Keith Weir)