Labour is on track to seize enough seats from Conservatives to become the largest party in Westminster after next year's general election, according to polling by a former Tory treasurer in the vital marginal constituencies which will determine the result.
But the survey carried out for Lord Ashcroft suggested that the number of voters switching directly from Tories to Labour is smaller in seats where Ukip is performing strongly.
The findings will fuel concern in Ed Miliband's party that any complacency about the impact on Labour of the rise of the eurosceptic Ukip could rob them of victory in the May 2015 poll.
In his latest poll of marginal seats, Lord Ashcroft questioned more than 1,000 voters in 11 Conservative-held constituencies which are not among the Tories' most vulnerable seats but where Labour took second place in 2010 and will be hopeful of winning next year as part of their drive to get Mr Miliband into 10 Downing Street.
The survey found an overall 5% swing from Tories to Labour in these seats - enough to snatch nine of them (Brentford & Isleworth, Brighton Kemptown, Corby, Enfield North, Halesowen & Rowley Regis, Hastings & Rye, Hove, Ipswich and Nuneaton).
Coupled with previous surveys in more marginal Tory-held constituencies, Lord Ashcroft said the results suggested at least 29 seats would fall to Labour if the findings were repeated at the general election.
But he said that the swing varied "significantly" depending on the Ukip presence in each seat, with a strong showing from Nigel Farage's party enough to deny Mr Miliband a lead in Pudsey and Gloucester and threaten his chances in Halesowen.
"Though nine of these seats would change hands on the basis of these snapshots, Labour will not feel comfortable in many of them," said Lord Ashcroft. "Though Labour led by 10 points in Enfield North and 13 points in Brentford, they were ahead by less than five points in Brighton Kemptown, Hove, Halesowen & Rowley Regis and Nuneaton.
"Swings to Labour appear to be related to the Ukip presence, which varied significantly from one seat to the next. Nigel Farage's party scored just 7% in Brentford & Isleworth, where Labour's share was up 11 points since 2010, but 24% in Halesowen, where Labour were down by two points, though still just ahead."
The Tory peer said the figures supported the theory that Ukip could hamper Labour in Tory-held target seats by diverting voters who might otherwise switch straight from blue to red.
The Liberal Democrat vote had fallen by more than half in all of the seats surveyed, with just 23% of those who voted Lib Dem in 2010 saying they would do so again next May.
:: Some 11,002 adults were interviewed by telephone in the 11 constituencies between September 10 and October 3.