According to the survey by ORB International released on Tuesday, 52 percent of the 2,000 respondents said they thought Britain should leave the EU, while 48 percent were in favor of it remaining in the bloc.
The poll, which was conducted last week, did not allow respondents to give an undecided response.
The result indicates a decline in the number of those wanting Britain to remain an EU member, with an ORB survey last month showing 53 percent in favor of staying.
ORB, which is commissioned to conduct surveys by the British paper "The Independent," said it was the first time a poll result had shown a majority wanting the so-called "Brexit" since it began polling on the question six months ago.
Young people EU-friendly
The poll showed that young people aged 18 to 24 were much more likely to want to remain in the EU than those in the 65-and-over age group, and that support for EU membership was strongest in Scotland and Wales.
British Prime Minister David Cameron, who says he supports British membership in the EU despite voicing his dissatisfaction in several areas, has pledged to hold a referendum on the matter by the end of 2017.
Recently, Cameron has angered several European leaders by demanding concessions that he says would increase British support for staying in the bloc. They include exempting Britain from certain economic regulations and reducing migration from some member states into the country.
Refugee crisis a possible factor
The "Independent" speculated in its Tuesday edition that the Paris attacks may have shifted sentiment toward a "Brexit." This is, however, disputed by some pro-EU campaigners, who say the November 13 attacks, claimed by self-named "Islamic State" jihadis, may well end up increasing British solidarity with the bloc.
Others say the refugee crisis is a factor that might be making some Britons feel they could be better off outside the EU - even though the UK is yet to take in any of the refugees heading for Europe.
Many observers say an exit of Britain from the EU could deal the bloc a severe, or even mortal, blow, with the country being the second strongest economy in Europe behind Germany.
Some British media are also predicting that such a move could result in Scotland seeking independence from London, with the dominant Scottish National Party a staunch supporter of EU membership.
tj/msh (dpa, AFP)