FOREX-Dollar edges up after poll shows tightening 'Brexit' vote

* Survey shows "Remain" camp gaining ground

* Euro, sterling fall after survey

* Markets as Draghi, Yellen address 'Brexit' risk (Recasts; adds data, quote, updates prices)

By Dion Rabouin

NEW YORK, June 21 (Reuters) - The dollar rose on Tuesday as investors sold the British pound and the euro on news that the gap had narrowed in the latest poll on Britain's referendum on European Union membership, with two central bank heads saying the so-called Brexit vote could have serious consequences.

The dollar rose against both currencies after a poll conducted by Survation for spread-betting firm IG (LSE: IGG.L - news) showed the percentage of voters supporting Britain's exit from the EU had risen to 44 percent from 42 percent in its previous poll on Sunday. A majority of respondents still preferred "Remain," but by just a 1 point margin, with 45 percent support.

The dollar added to those gains after testimony from Federal Reserve Chair Janet Yellen and European Central Bank President Mario Draghi.

Draghi said during his speech at European Parliament that uncertainty in the euro zone is high, partly due to Britain's June 23 referendum, and that the ECB was ready to act with all instruments if necessary. He also said that "further monetary policy stimulus (was) in the pipeline."

That spooked markets, said David Gilmore, partner at FX Analytics in Essex, Connecticut, but that was because many investors misinterpreted Draghi's remarks.

"Markets read that as there's going to be more quantitative easing or asset purchases on a monthly basis or interest rates are going to be more negative or both," Gilmore said. "That's not what he said. But the move happened and people bought dollars and sold euros on that headline."

The euro fell 0.55 percent to $1.1252, holding just above a session low of $1.1243.

The dollar index, which measures the greenback against six major world currencies, rose 0.45 percent to 94.031.

Sterling turned negative against the dollar after the release of the Survation poll and fell further, inching toward session lows, during Draghi's speech. It (Other OTC: ITGL - news) was last down 0.25 percent to $1.4654.

Sterling had earlier climbed its highest since early January against the dollar after the release of two earlier 'Brexit' opinion polls that indicated the "Remain" camp had regained some ground.

Yellen also addressed the risk of a Brexit vote, saying that before a further tightening of monetary policy, the Fed needs to be sure U.S (Other OTC: UBGXF - news) . economic growth and hiring have rebounded and there is no shock from the outcome of Britain's vote.

(Reporting by Dion Rabouin; editing by Nick Zieminski and Diane Craft)