By Jemima Kelly

LONDON, May 25 (Reuters) - Sterling climbed to a 3-1/2-month high against the euro on Wednesday as several bookmakers shortened the odds on Britain voting to stay in the European Union to 1/7, indicating around an 85 percent chance of that outcome.

Most economists and strategists reckon a vote to leave - or a "Brexit" - at a referendum on June 23 would deal a blow to Britain's economy and would send sterling tumbling.

Ratings agency S&P said on Wednesday that a Brexit could "jeopardize sterling's position as a reserve currency and the associated benefits to the 'AAA' credit rating".

With investors trying to work out how likely that eventuality is, opinion polls present a confusing picture, with some saying the "In" camp has a big lead and others putting the two sides neck-and-neck. The latest, from YouGov on Wednesday, showed Britons evenly split.

So with less than a month to go before the referendum, bookies are offering something to investors that the polling industry has failed to provide: a clear trend, having consistently shown that a "Brexit" is unlikely to happen.

Sterling strengthened to 76.01 pence per euro on Wednesday, its strongest since early February. Against the dollar, the pound hit $1.4665, its highest since May 3.

"After the pound's recent rebound, the market is now pricing in a more modest Brexit risk premium which is likely to result in a more modest initial bounce higher should the UK vote to remain within the EU," said Bank of Tokyo-Mitsubishi UFJ currency strategist Lee Hardman.

Worries about a Brexit drove the pound down 11 percent on a trade-weighted basis between mid-November and early April, when it hit a 2-1/2-year low. But it has recovered around half of that as investors price out chances of a rate cut that some were factoring in if Britain opted to leave.

Bank of England Governor Mark Carney said on Tuesday that there was a "higher bar" in drawing conclusions about the economy due to substantial uncertainty around the Brexit referendum, noting that the BoE would be able to deal with any fallout from the vote.

He also said that it was not clear whether the bank would cut interest rates if the economy slowed after a possible Brexit, but said leaving the EU would reduce the probability that the next move in rates would be up.

"Considering it remains our main case that the UK will stay part of the EU, we believe that sterling dips may still prove an attractive buy, in particular against currencies such as the Swiss franc or the Norwegian crown," Credit Agricole currency strategists wrote in a note to clients.

The cost of hedging against sterling weakness over the coming two months has fallen as worries about a Brexit have eased. Two-month sterling/dollar implied volatility has fallen to around 14 percent, having traded as high as 17.75 percent earlier this month.

(Editing by Hugh Lawson) ((jemima.kelly@thomsonreuters.com)(+44 0 20 7542 7508)(Reuters Messaging: jemima.kelly.thomsonreuters@reuters.net))