The online poll by YouGov showed that 56 percent would be in favour of leaving and 44 percent in favour of staying, excluding those who did not know or would not vote.
Britain has won the Eurovision five times since it was first staged in 1956, making it joint third on the list of winners along with France and Luxembourg.
But many Britons complain that in recent decades their contestants have been unfairly overlooked and left near the foot of the leaderboard and the dreaded "nul points".
In last year's EU membership referendum, 52 percent of Britons who cast their ballots voted to leave the European Union while 48 percent wanted to stay.
The poll found roughly the same dividing lines.
Those who wanted to leave Eurovision included 76 percent of people who voted for Brexit, 81 percent of those who intend to vote for the anti-EU UK Independence Party at the upcoming general election and 78 percent of people aged 65 and over.
Those who wanted to stay included 65 percent of those who voted to remain in the European Union, 70 percent of those who intend to vote for the pro-EU Liberal Democrats and 69 percent of 18-24-year-olds.
First and second on the list of Eurovision winners are Ireland and Sweden.
Britain's only victory since 1981 was in 1997 with Katrina and the Waves performing "Love Shine a Light".
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