The poll focused on 40 of Britain's 650 parliamentary seats where Cameron's Conservative party won with the slimmest of margins at the last national election in 2010.
According to polling data from Lord Michael Ashcroft, the billionaire former Tory party deputy chairman, the main opposition Labour party had made little progress in the constituencies despite being ahead in opinion polls nationwide.
But a surge in support for the UK Independence Party (UKIP) was siphoning off support from the Conservatives, pointing to a Labour election victory, the poll showed.
If an election were held today, Labour would win 32 of the 40 battleground seats surveyed and would win overall power in Britain with a majority of about 60%, it said.
The survey, the first of its kind in two years, will worry the Conservatives who are preparing for their annual conference and have cut Labour's lead in some opinion polls to just three percentage points nationwide at a time when the economy is showing signs of recovery.
But Lord Ashcroft said the new data showed the underlying picture was more complex and that the Conservatives faced a "formidable" challenge to stay in government, let alone win an overall majority.
The Conservatives govern in coalition with the smaller Liberal Democrat party.
"The picture is seldom uniform across the country; the national headline figures can sometimes mask what is happening in marginal seats where elections are won and lost," he said.
"Labour's lead in these seats has grown from nine to 14 points over the last two years, largely because of the defection of Tory (Conservative) voters to UKIP," he said, noting UKIP had tripled its share of votes in such marginal seats since 2010.
Anti-EU, Anti-immigration
UKIP, which has no seats in the British parliament but is represented in the European Parliament, campaigns for Britain to leave the EU and for an end to what it calls "open-door immigration".
It has tapped into public disenchantment with what many Britons regard as the EU's excessive influence over their lives and into fears that immigration levels are too high.
The party did well in local elections earlier this year, winning one in every four votes cast, and is forecast to do well in European Parliament elections next year.
But Britain's "winner takes all" election system means it is unlikely to win a large number of seats in the national parliament in 2015.
Some lawmakers in Cameron's Conservatives want him to forge an electoral pact with UKIP to guard against a split vote and are likely to increase their calls for him to do so before 2015.
But Cameron and Nigel Farage, UKIP's leader, have had strained relations since 2006 when the Conservative leader said UKIP was full of "fruitcakes, loonies and closet racists".
Responding to pressure from within his own party and UKIP, Cameron earlier this year promised Britons an in/out EU referendum by the end of 2017 if re-elected.
Nearly 13,000 people were surveyed for the poll.
