Betting odds indicate UK "Out" campaign making up ground fast

* For a graphic of opinion polls: http://tmsnrt.rs/1Ke31HF

* Betfair: 64 percent chance of an In vote

* William Hill (Other OTC: WIMHF - news) : 69 percent chance of an In vote (Adds details on odds)

LONDON, June 13 (Reuters) - The chances that Britain will vote to leave the European Union increased sharply on Monday to 36 percent, the highest level since the June 23 referendum was announced by Prime Minister David Cameron four months ago, according to betting odds.

The implied probability of a British vote to stay in the EU fell to as low as 64 percent, down around 14 percentage points from last Thursday when the probability was 78 percent, according to betting odds supplied by Betfair.

Odds moved after an opinion poll by ORB for The Independent newspaper showed the "Out" camp was 10 points ahead of "In".

Bookmaker William Hill said it was offering its shortest ever odds - 7/4 or a 36 percent implied probability - on the chances of a vote to leave the European Union.

"We had to halve our odds on Monday morning for a Brexit result," William Hill spokesman Graham Sharpe said.

"Political punters betting with William Hill that the EU Referendum will produce a 'Leave/Brexit' outcome have forced the odds down to their shortest level since the date of the vote was confirmed back in February," Sharpe said.

William Hill said it was offering 4/9 for a bet on an In vote, or an implied probability of 69 percent.

Opinion pollsters who failed to forecast both Prime Minister David Cameron's unexpectedly decisive election victory and the result of Israel's election last year have so far painted contradictory pictures of British public opinion.

A British exit would rock the European Union -- already shaken by differences over migration and the future of the euro zone -- by ripping away its second-largest economy, one of its top two military powers and by far its richest financial center. (Reporting by Guy Faulconbridge; editing by Stephen Addison)