The poll by Tory peer Lord Ashcroft gives Labour a two-point advantage over the Conservatives in Finchley and Golders Green -- still well within the margin of error. Lawyer Sarah Sackman is the Labour candidate for Finchley and Golders Green, hoping to remove Tory incumbent Mike Freer.
The poll 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.
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Thatcher and her husband Denis waves to supporters after she retained her Parliamentary seat of Finchley in North London, Friday, May 4, 1979
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.
On Tuesday, David Cameron held out the prospect of free childcare for working families and a "tax free minimum wage" as he declared the Conservatives were the "real party of working people". Unveiling the Conservative election manifesto, the Prime Minister said that after the years of recession and austerity the "good life" was finally at hand as he urged voters not to allow Labour to return the country to "square one".
He said that if the Tories were returned to power after polling day on May 7 they would double the existing free childcare provision for three and four-year-olds saving parents £5,000 a year. A Conservative government would also legislate to ensure no-one on the minimum wage would pay income tax - automatically uprating personal allowances in line with increases to the basic rate of pay.
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David Cameron unveils his party's general election manifesto in Swindon, southern England, on April 14, 2015
Together with the extension of Thatcher's Right to Buy scheme to 1.3 million housing association tenants - announced overnight - and the promise to lift family homes worth over £1 million out of inheritance tax, they formed the centrepiece of the Conservatives' pitch to voters.
"At the heart of this manifesto is a simple proposition," Cameron said at the launch in Swindon, Wiltshire. "We are the party of working people, offering you security at every stage of your life."
Lord Ashcroft Polls interviewed between 1,000 and 1,002 adults in each constituency by telephone between April 2 and 11.
Below are pictures of Margaret Thatcher in her Finchley constituency
Thatcher In Finchley
(01 of18)
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Margaret Thatcher, Conservative candidate for Finchley. (credit:Barratts/S&G and Barratts)
(02 of18)
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Margaret Thatcher 34, Conservative candidate for Finchley, is introduced to darts in a local pub by Fred Booth, a Finchley greengrocer. Mrs Thatcher aims to be the first woman barrister to be an M.P. (credit:PA/PA Archive)
(03 of18)
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Margaret Thatcher, Conservative MP for Finchley (credit:Barratt's/S&G and Barratts)
(04 of18)
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Margaret Thatcher MP enters the House of Commons after being elected member for Finchley in the General Election (credit:Barratts/S&G and Barratts)
(05 of18)
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Recently elected Conservative MP for Finchley and Friern Barnet, Margaret Thatcher, 33, with her twin children, Carol and Mark, aged 6, at their home in Farnborough, Kent. (credit:PA/PA Archive)
(06 of18)
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Mrs Margaret Thatcher, who succeeds Sir Edward Boyle as spokesman for Education in the Conservative Shadow Cabinet, at the Houses of Parliament. The change was announced by Mr Edward Heath. (credit:PA/PA Archive)
(07 of18)
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Margaret Thatcher shopping in a supermarket in her Finchley constituency, North London. (credit:PA/PA Archive)
(08 of18)
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Margaret Thatcher, the Prime Minister, shopping in a Finchley supermarket, London, part of her constituency. (credit:PA/PA Archive)
(09 of18)
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Newly elected MP for Finchley and future British Prime Minister, Margaret Thatcher celebrated her victory with her 21 year-old son Mark, 11th October 1974. (credit:Sydney O'Meara via Getty Images)
(10 of18)
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Margaret Thatcher, the Conservative M.P. for Finchley and Friern Barnet, is shown Nov. 1959 at her Farnborough, Kent, England, home with her twins, Mark and Carol, aged six. (credit:ASSOCIATED PRESS)
(11 of18)
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British Prime Minister Margaret Thatcher crouches down to get an eye level view of one of the displays when she visited a supermarket at Finchley in north London on Saturday, May 22, 1983. (credit:ASSOCIATED PRESS)
(12 of18)
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Mrs. Margaret Thatcher, Barnet, Finchley MP who believes in stocking up her larder shelves, places an empty shopping basket in the boot of her car, parked outside the House of Commons, Westminster in England on the eve of the Conservative party's leadership election on Feb. 3, 1975. (credit:AP)
(13 of18)
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Margaret Thatcher, who succeeds Sir Edward Boyle as spokesman on Education in the Tory Shadow Cabinet, is shown at the Houses of Parliament, Oct. 22, 1969. (credit:ASSOCIATED PRESS)
(14 of18)
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The lady in red chiffon is Conservative Party leader, Margaret Thatcher at her London home, Feb. 1, 1976, prior to leaving for her meeting with constituents at Barnet, Finchley. (credit:ASSOCIATED PRESS)
(15 of18)
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Tory leader Margaret Thatcher holding up five one-pound notes during a speech on April 30, 1976 at the Conservative headquarters in her Finchley, North London, constituency. (credit:ASSOCIATED PRESS)
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A library picture taken of Conservative Party leader Mrs. Margaret Thatcher in a jubilant mood outside her Chelsea, London, home in November 1976, after Tory victories in by-elections at two former Labour strongholds â Workington and Walsall North. (credit:ASSOCIATED PRESS)
(17 of18)
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Mrs. Margaret Thatcher and her husband Denis, at The Town Hall in London's Hendon, Friday, May 4, 1979 where she heard she had been re-elected at Finchley with a big increase in majority. (credit:ASSOCIATED PRESS)
(18 of18)
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Conservative Party leader Mrs. Margaret Thatcher, wearing a fire chief's helmet during a visit to the London Fire Brigade's Finchley fire station in London, in October 1979. (credit:AP)