Labour has received a bounce in the polls days after the release of the party's general election manifesto.
The party is up 8 points in the latest Ipsos Mori poll, compared to a similar survey last month.
However, Labour still trails the Conservatives by a whopping 15 points.
Despite the size of the gap the result will add to Tory nerves about June 9.
The Conservatives had hoped that to secure a landslide victory at a snap election.
But party sources fear a combination of factors could mean the party takes fewer seats than expected.
Mrs May has urged voters to send her as many Tory MPs as possible, claiming that a large majority in the House of Commons would strengthen her hand in Brexit negotiations with Brussels.
But opposition parties have called on the electorate not to give her a "Margaret Thatcher-style" dominance over parliament, claiming that would see Common's ability to hold her to account "go out of the window".
The poll, commissioned by the Evening Standard newspaper, found the Conservatives steady on 49 per cent, with Labour up 8 points to 34 per cent.
But support for the Liberal Democrats halved to 7 per cent, while Ukip fell to just 2 percent.
Meanwhile, Labour leader Jeremy Corbyn said that high earners would not be hit with an immediate tax rise if Labour wins the keys to Downing Street.
The party plans to raise £6.4 billion by lowering the threshold at which workers start paying the 45p rate of income tax, from £150,000 to £80,000, and by introducing a new 50p rate above £123,000.
Mr Corbyn said that the changes would be phased in over the course of the next parliament, which will end in 2022.
He told the BBC’s Jeremy Vine show: "I'm not saying how much they are going to actually have to pay straight away, we will put it up during the parliament."
Mr Corbyn defended his tax plans, which include a guarantee of no hikes to VAT, personal national insurance contributions or income tax for 95 per cent of workers, and insisted it was "reasonable" to ask for more money from the highest earners.
"If you are earning at the very top end I think it is reasonable that you make a slightly larger contribution to our society's needs," he said.
"What we have said is the majority of our funds we want will come from corporate taxation and will come from dealing with the issues of tax evasion and placing profits in convenient tax regimes where very little tax is paid."
Later Mr Corbyn visited a Sikh temple, a day after Boris Johnson angered a follower of the faith by discussing whisky exports on a similar visit.
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