An ICM survey for The Sunday Telegraph put the Conservatives on 38 percent, ahead of Prime Minister Gordon Brown's Labour Party on 31 percent and the Liberal Democrats on 21.
The Conservatives are bidding to end 13 years of Labour rule. But the Conservative lead is down from nine points last month and equals its lowest in any ICM poll for the last two years.
If the result were to be repeated at the election, widely expected on May 6, the Conservatives would be the largest party in parliament but still 30 seats short of an overall majority.
It is the latest in a series of polls pointing to Britain's first hung parliament since 1974.
Financial markets fear a minority or coalition government would be reluctant to take the strong action investors want to cut Britain's budget deficit, forecast to reach 178 billion pounds this year.
The British pound has been buffeted by the opinion polls. Sterling rose against the dollar on Friday after a poll suggested the Conservatives would win an outright majority.
Markets punished the pound earlier this month after a poll showed Labour could stay in power but without a clear majority.
A hung parliament could leave the smaller opposition Liberal Democrats as kingmakers with either the Conservatives or Labour needing their support to pass laws.
The Conservatives want immediate action to start reining in the deficit while both Labour and the Liberal Democrats think the economy is t
oo fragile to withstand public spending cuts now and that they should wait until the 2011-12 financial year.
Liberal Democrat leader Nick Clegg indicated on Saturday that, if the Conservatives were dependent on Liberal Democrat support to form a government after the election, the Liberal Democrats would resist early spending cuts.
"We think that merrily slashing now is an act of economic masochism. If anyone had to rely on our support and we were involved in government of course we would say: 'No, do it sensibly ... Do it at a time when it is economically sustainable,'" he told the BBC.
Clegg's comment could reinforce investors' fears that a hung parliament would lead to inaction on government spending.
The Liberal Democrats said however they were confident markets would give politicians time to form a government if there was no outright winner.