By Simon Jessop and Maiya Keidan

LONDON (Reuters) - Britain's vote on whether to stay in the EU is high noon for the last remaining bears -- the few fund managers still brave enough to hold short positions betting that share prices will fall -- who could get swamped by a rally if Britain votes to stay in.

Demand to short shares in the FTSE 100 fell 2.75 percent between June 17 and June 21, according to data from FIS' Astec Analytics, as many traders opted to reduce risk heading into the vote.

"Short sellers are reducing their exposures to a market bounce in blue-chip stocks post the Thursday vote," said David Lewis, senior vice president at FIS' Astec Analytics.

That is part of an overall trend to reduce short positions which has been under way since early this year, JPMorgan said in a note to clients on Wednesday.

"There is a very distinct move from being net short (January-February) to net covered since March 2016. This can be interpreted as a reduction in risk appetite. The reduction took place across most sectors, the only exception being utilities," it wrote.

But a handful of hedge funds still have big short positions open. That means they could earn a windfall on those bets if Britain votes to leave and share prices tumble, but could face big losses if it stays in and shares rise.

Data from the Financial Conduct Authority, Britain's financial regulator, showed 134 asset managers worldwide had 427 short positions on 199 British firms, worth more than 0.5 percent of a company's value as of the close of markets on Tuesday.

BlackRock was by far the biggest, with 51 big short positions, followed by AQR Investment Management with 27 and Odey Investment Management with 17. Odey's boss, Crispin Odey, is a noted pro-Brexit campaigner.

None of the funds was available for comment on their Brexit exposure.

Short sellers borrow shares and sell them, betting that the price will fall and they can buy them back more cheaply later to return them to the lender. If prices rise, the potential losses can be huge, since the shares must be repurchased at a loss.

Among the targets of short trading recorded by the FCA are services firm Carillion <CLLN.L> and supermarket chains Ocado Group <OCDO.L>, Sainsbury <SBRY.L> and WM Morrison Supermarkets <MRW.L>. The targets include 37 companies from the FTSE 100.

Some of those bets may have been placed months ago based on factors other than Brexit, and some of the fund managers may have balanced their short positions with long positions in other securities that would reduce the Brexit risk.

The FCA said its data included 99 new short positions above the 0.5 percent disclosure threshold taken in the past week, slightly more than the 91 bets placed the week before.

The risky short bets have already been more exposed than usual because of the high volatility in the run-up to the Brexit vote.

Over the last 10 trading days, for example, 6 have seen the FTSE 100 move more than 1 percent - twice to the downside and 4 times to the upside.

(Graphic by Stephen Culp; editing by Peter Graff)