(Recasts with jump in sterling)

By Patrick Graham

LONDON, April 26 (Reuters) - Sterling pushed above $1.45 to its highest since mid-February on Tuesday, extending a week of gains due to growing expectations among investors that the push to withdraw Britain from the European Union will fail.

The cost of hedging against sharp swings in sterling caused by nerves in the run-in to the vote hit 6-year highs as options contracts moved to capture the result of the "Brexit" vote on EU membership on June 23.

But those moves came after implied volatility - the chief vehicle speculative investors have used to bet on trouble for the pound around the vote - fell by its most in a year on Monday.

Investors worry that a Brexit would leave Britain exposed to the risk of a currency crisis and problems in financing its huge public debt, while weakening a still shaky economic recovery.

Dealers said that, and the pound's steady gains in the past week, stemmed chiefly from a reduction in bets put on by hedge funds since February.

"People have been cutting positions that haven't been making money," said the head of hedge fund sales with one large international bank in London.

"But we have also seen some bets on the top-side. Its not just macro-type funds, we've seen equity funds positioning more for a remain vote and the bounce that will cause."

The pound gained 0.4 percent against both the euro and the dollar to trade at 77.57 pence and $1.4538 respectively.

Two-month sterling/dollar options , for the first time covering the vote and the result a day later, rose from around 11 percent to 14.40 percent, the highest level since mid-2010.

But three-month pricing has come down from highs around 16 percent to 13 percent. Two-month sterling/dollar risk reversals-- a gauge of bets on a currency rising or falling -- also show a lesser bias for sterling weakness against the dollar, trading little changed from Monday at 1.5 vols.

The latest poll on Tuesday, by the ORB organisation for The Daily Telegraph newspaper, showed support for remaining in the European Union declined by 2 percentage points to 51 percent over the past week.

The first poll to be taken after an appeal last week by U.S. President Barack Obama for Britain to stay in the 28-country bloc is not due until Wednesday.

"Somewhat stabilizing expectations when it comes to the June EU referendum seems to increase uncertainty among all those who are short the currency," Credit Agricole analysts said in a note pointing to the potential for sterling to gain further.

"(But) it is still early days and real demand is unlikely to return until a positive outcome in June."

(Additional reporting by Anirban Nag; Editing by Raissa Kasolowsky) ((anirban.nag@thomsonreuters.com; +44 20 7542 8399 ; Reuters Messaging: anirban.nag.thomsonreuters.com@reuters.net))