LONDON (Reuters) - British voters may opt to leave the European Union if Prime Minister David Cameron holds a referendum on membership as early as June, Scottish nationalist leader Nicola Sturgeon has said, The Scotsman newspaper reported on Wednesday.

Scotland's First Minister Nicola Sturgeon arrives at 10 Downing Street to meet Britain's Prime Minister David Cameron in London, December 14, 2015. REUTERS/Toby Melville

Cameron is pushing for a deal on new membership terms from other EU leaders before a referendum which he could call this summer, though opinion polls have shown that opposition to the European Union is growing in Britain.

Sturgeon was quoted by The Scotsman newspaper as saying that if the referendum was called in June there might be too little time to convince voters in the rest of Britain that EU membership was the right choice.

“It would leave barely four months – including the period of the Scottish election – for the public to fully engage in and for the arguments about EU membership to be heard fully,” she told a news conference, according to the report.

“David Cameron needs to get away from the very narrow focus on these renegotiation issues and make the big picture case for staying in,” Sturgeon was quoted as saying.

Sturgeon, leader of the Scottish National Party and of Scotland’s devolved government, said she was confident Scotland would vote to stay in the EU, but was now less sure about what the rest of the United Kingdom would decide, the paper reported.

Scotland has 5 million people, compared with England which has 53 million and represents about 84 percent of the population of the United Kingdom.

Scots voted 55-45 percent against independence in a referendum in 2014, but Sturgeon’s party then won 56 of the 59 seats representing Scotland in the national parliament in London in an election last May.

Scottish nationalists have repeatedly told Cameron that he cannot rule out giving Scotland another independence referendum, and that a situation in which Scots voted to stay in the EU but a majority of all Britons voted to leave could be a trigger.

Sturgeon has previously said there could only be another independence vote if a majority of Scots voted for a party which proposed one in a Scottish parliamentary election. Such an election is due in May this year.