By Peter Griffiths
LONDON (Reuters) - A majority of British voters would choose to stay in the European Union if Prime Minister David Cameron succeeds in renegotiating London's ties with the 28-nation bloc, a poll found on Tuesday.
Cameron promised in January to try to reach a new settlement with the EU before holding an in/out referendum by the end of 2017, provided he wins the 2015 election.
While surveys suggest Britons would vote to leave if they were given a say today, the YouGov survey for the Sun newspaper said the Conservative prime minister could persuade a majority to vote to remain in the bloc if he secures a new deal.
Fifty-two percent would vote to continue Britain's 40-year EU membership on new terms, 28 percent would opt to leave, 16 percent were undecided and four percent would not vote.
Asked how they would vote if a referendum were held now, before Cameron begins his renegotiation, there was an even split, with 39 percent wanting to stay and 39 percent in favor of leaving.
Cameron said last week that "consent for remaining inside the EU is wafer thin", and that his European reform plan had the overwhelming support of voters and business leaders.
His government is reviewing the balance of powers held between London and the EU. Cameron has spoken of cutting EU regulation and repatriating powers in areas such as employment law, law-and-order and social policy.
The Labour opposition, which has a seven-point lead over Cameron's Conservatives, has accused him of being forced to offer a referendum to placate rebellious anti-EU Conservatives and to stem a loss of support to the UK Independence Party (UKIP), which wants Britain to leave the EU.
Anti-EU campaigners see the bloc as an expensive, wasteful and over-powerful threat to British sovereignty.
Their opponents say it would be economic suicide for Britain to leave a single market of 500 million people and that Britain should try to reform the EU from within.
YouGov questioned 1,752 adults on November 10-11.
(Reporting by Peter Griffiths; Editing by Mark Heinrich)