A poll of Conservative-held marginals has shown the Tories trailing or tied with Labour in five of the 10 seats surveyed.
Finchley and Golders Green in north London - where Margaret Thatcher was once MP - is one of three seats where Labour is now ahead, according to the poll by Tory peer Lord Ashcroft.
The poll gives Labour a two-point advantage over the Conservatives in the constituency - still well within the margin of error.
It also puts Labour three points ahead in Crewe and Nantwich, which the Conservatives took from Labour in a by-election in 2008, and two points ahead in Milton Keynes South.
There were ties in Rossendale and Darwen - where the Tory vote was unchanged from the 2010 general election but Labour's Will Straw, son of former Labour minister Jack, is up 10 points - and South Ribble.
The Conservatives are ahead in the other five seats surveyed: Cleethorpes, where they have a narrow two-point advantage, Dover, Dudley South, Harlow, and North East Somerset, where Jacob Rees-Mogg is 16 points clear of Labour.
The findings will hearten Labour amid a welter of contradictory polling evidence which suggests that so far neither of the two main parties has been able to make a decisive breakthrough in the election battle.
:: Lord Ashcroft Polls interviewed between 1,000 and 1,002 adults in each constituency by telephone between April 2 and 11.