By Dion Rabouin

NEW YORK (Reuters) - The dollar tumbled on Monday as sterling surged toward its largest one-day percentage gain since 2008 after opinion polls swung in favor of the campaign for Britain to stay in the European Union, boosting risk sentiment.

Investors reacted after three of six opinion polls published during the weekend showed a shift toward keeping Britain in the EU, with some citing the killing last week of pro-EU lawmaker Jo Cox as a factor.

The implied probability of a "Remain" vote in Thursday's referendum rose to around 78 percent after falling as low as 60 percent last Thursday, according to odds from gambling website Betfair.

"This was the first time that we’ve seen a poll that was conducted over the period after (Cox) was tragically killed," said Scott Smith, senior corporate FX trader and market analyst at Cambridge Global Payments in Toronto. "So given the sentiment has changed and it’s looking more likely that Britain will remain within the EU, we’re seeing a rally in risk-correlated assets along with the sterling."

Stocks and other riskier assets rose while traditional safe-havens fell in a reversal of the risk-off trading that has dominated markets for much of June.

European shares <.FTEU3> rose 3.66 percent while the U.S. S&P 500 stock index was up 0.8 percent <.SPX>.

Sterling briefly fell back as rumor-driven speculation emerged about forthcoming polling data that could show the "Leave" camp pulling ahead of "Remain" in the UK's June 23 referendum.

"There's still some jitters out there," said Thierry Albert Wizman, global interest rates and currencies strategist at Macquarie Ltd in New York.

Prior to the brief selloff, sterling <GBP=D4> rose to a global session high of $1.4707, nearly a three-seek peak, as it extended a recovery from Thursday's more than two-month trough of $1.4013.

Sterling was last up 2.3 percent at $1.4688, its largest one-day rise since Dec. 15, 2008.

The pound gained 2.3 percent to 152.65 yen <GBPJPY=R>, pulling away from a three-year trough around 145.34, also on Thursday. The euro fell 1.9 percent to 77.12 pence <EURGBP=D4>.

The dollar <.DXY> fell against a basket of major currencies, dropping to 93.449 in early trading, its lowest in more than two weeks. It was last down 0.6 percent at 93.654.

The euro rose 0.1 percent to 117.60 yen <EURJPY=R>, well above Thursday's three-year low of 115.51 yen. Against the dollar, the euro gained 0.3 percent to $1.1309 <EUR=>.

(Reporting by Dion Rabouin; Additional reporting by Anirban Nag and Lisa Twaronite in London; Editing by Bill Trott and Steve Orlofsky)