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The new Ipsos-Mori poll, commissioned by London's Evening Standard newspaper, found 55 percent of those surveyed supported staying in the EU, while 37 percent wanted to leave, just over a month before the June 23 referendum.
Sterling strengthened to 77.825 pence per euro after the poll's release, having traded around 78.17 pence beforehand.
And having been down against the dollar all morning, sterling strengthened to $1.4483 after the poll, leaving it up 0.1 percent on the day.
According to betting website Betfair, the implied probability of a British vote to stay in the European Union rose to 76 percent after the poll, up from 73 percent.