LONDON (REUTERS) - British Prime Minister David Cameron said on Friday he would not quit if Scotland voted to leave the United Kingdom in a September referendum to become an independent country.

Asked if he would resign if he presided over the break-up of the United Kingdom, Cameron said the Sept 18 vote would not determine his future as prime minister or Conservative leader as that would be decided at Britain's general election next May.

"I believe, as prime minister, I did the right thing by enabling this vote to go ahead, but the vote is about whether Scotland stays in the United Kingdom or separates itself from the United Kingdom," Cameron told BBC Radio. "It's not about my future, it's about Scotland's future."

His comments came after reports he had told this to allies in an effort to ensure Scots did not use the referendum to try to punish him or the Conservative party, which is unpopular in much of Scotland.

All three major UK political parties are campaigning to preserve Scotland's 307-year-old union with England, but Cameron is likely to face most of the blame if Scotland leaves as he approved the referendum in 2012, believing the vote would fail.

Recent polls have shown a gradual increase in support for independence, eroding a strong lead enjoyed by the "No" campaign although the nationalists still have ground to catch-up.

An ICM poll last month found 42 per cent of voters intended to vote no and 39 percent would vote in favour of independence while 19 per cent remained undecided.

Other polls have shown a wider gap.

Cameron, whose Conservative party holds only one Scottish seat in the Westminster parliament, said he believed he had shown "respect" to Scottish voters by offering them a referendum which was "legal, decisive and fair". "In the end, you can't hold people in an organisation against their will," Cameron said. "So I think I have taken the right decision to answer these questions about Britain's future, rather than duck them."