Support for Scotland to break away from the rest of the United Kingdom has risen to 40 percent, according to one opinion poll published on Tuesday, as nationalist leader Alex Salmond headed into a U.S.-style television debate on secession.

Scotland votes in a Sept. 18 referendum on whether to end its 307-year union with England, though some polls suggest that as many as a quarter of Scotland's 4 million voters remain undecided.

A poll from Ipsos Mori showed support for independence rose to 40 percent, up 4 percentage points since a similar poll in June and the highest support that the pollster has yet recorded for the "Yes" campaign.

Polls show different levels of support for the "Yes" campaign, although none show the campaign for independence in the lead and it has struggled to make any headway since the end of March.

The Ipsos Mori poll found that 54 percent were set to reject independence, unchanged since June, while 7 percent of the electorate were still unsure about how they would vote — a 3 point fall.